This is my re-post from ELI5 but I think I’d get more precise answers from here. I understand there where different forms of slavery ranging from the US to Romans and Nordic Vikings but any answer from any era will be appreciated. I’m just trying to gather a sense of the different forms of ‘confirmation’ whether it was by a letter or public announcement etc.
For freed slaves in antebellum Maryland, the county courts would issue "freedom certificates" - essentially an identification card that stated that the bearer was a free person. The Maryland State Archives has digitized a large number of the surviving registers of freed persons here.
Here is an example: Maryland Anne arundel County to wit: I hereby certify to all whom it doth or may concern that it hath been proved to my satisfaction that the bearer hereof a woman named Fanny about twenty two years old five feet high and of a dark complexion is a free woman and that her freedom commenced on the 25.th day of December 1809 said Fanny was raised in the County aforesaid Issued the 27 November 1810
The concern with these documents was that they could be forged. Often runaway advertisements for slaves included notes on the enslaved person's literacy. If the slave could write, or if he had family that could write, or if he made off with enough valuables to buy a forged pass were all concerns of the advertising master.
Despite issuing freedom passes, freed slaves or people born free were still harassed or imprisoned on the belief that they were enslaved. Jailers across the south bought advertisements in their local (or regional) newspapers advertising that they had caught a suspected runaway. Typically, these advertisements included descriptions of the captured person, their name, and the name of their "master". In some cases, the advertisement stated something along the lines of "His Master, if any, is desired to take him away and pay Charges..." (MD Gazette, 11/7/1771). If a freed person had a large family or was well known in the area they lived, they were less likely to be harassed, as they would have support from the community. Typically, if an enslaved person was able to achieve their freedom through legal means (in other words, not running away to a 'free state' but instead being manumitted or purchasing themselves, or winning their freedom in a suit), they were less likely to be assaulted with charges that they should be enslaved, largely because they would both be well known in their home town/region and because there was respect for the legal means of freeing an enslaved person. As the nineteenth century progresses, slaves' routes to freedom were either made stricter or eliminated altogether because of the concerns of the northern attack on slavery, and the heightening tensions between whites and freed people of color.
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I'm afraid I can't speak to ancient contexts, but I can offer you an answer for slavery as it was practised in the United States and the British Caribbean. This is going to be quite a broad overview because you seem interested in general principles and there's quite a lot of variation in how manumission worked at different times and places in the New World. If you'd like more detail on anything or anywhere/when in particular, let me know!
I think there are really two questions here:
So first and foremost, it's important to understand that the practice of someone being able to purchase their freedom was extremely rare under racial slavery as it was practised in the New World. It did happen, but it was not even an option for the vast majority of enslaved people in either the United States or the Caribbean. As far as the law and society were concerned, enslaved people were property and had no autonomous will of their own that could be recognised in law (this is not an exaggeration - the Alabama Supreme Court quite literally made a ruling like this in 1861). Although by the 19th century people held as slaves did enjoy a number of theoretical, bare minimum legal protections (like the right not to be deprived of life without due process of the law), they were limited in scope and intended only to create the impression that slavery was a benign institution. They were not intended to give slaves any kind of right to self-determination or limited freedom, only protection from excessive violence or exploitation. And on the ground, all kind of additional restrictions (some legal, some unofficial) made these legal entitlements by and large completely worthless, as we know from the rich body of testimony (both from enslaved people and white observers) that affirms how widespread extreme and lethal violence was under slavery. The limited legal identity that enslaved people had only really existed in the area of criminal law, and was almost exclusively only ever recognised when a slave was accused of wrongdoing - not when they were accusing someone else (which was often legally impossible).
If you were held in slavery, then you would not receive any kind of financial compensation for the labour you performed; the whole point of this system is that your owner claims a right to exploit your labour for their economic and social benefit. If you had ambitions to purchase your own freedom, then you were going to have to find the means to do so outside of the context of your services to your legal owner. In most cases, this meant hoping that you might be 'hired out' to someone else by your owner to work for them for a period instead. There was a large market in the United States especially for slave-labour-for-hire, where one person would agree to 'rent out' the labour of an enslaved person to someone else. This 'hiring-out' could take many forms: it might be a one-day trip to do a simple task, or it could be for weeks or months at a time. Often 'hiring-out' involved enslaved people who had knowledge of a trade - like carpentry for example - being sent to do skilled work for someone else who did not have such knowledge in their work-force. Particularly in urban environments, you might find enslaved people hired out to perform all kinds of menial and labour-intensive tasks in the urban economy, public service provision (like refuse collection) or domestic service. Plantations did also hire out parts of their work-force to other farms, but the scope and frequency of this in any area would depend on a number of factors.
But no individual enslaved person had any kind of direct involvement in negotiating these contracts of temporary employment. They are the object of the transaction, not a party to it - as far as slave owners were concerned, economically and morally, renting one of their workers out to another person or group was no different than renting out a room in one's house. The person being made to do this work had no say in the matter unless their master wanted voluntarily to give them one, and they had no entitlement to benefit from the transaction. If you were hired-out as a slave, you were not paid for your labour and your efforts - your owner was compensated for renting you as property. It was entirely up to your owner whether or not they would see fit to let you keep a share of the payment they received for yourself, or if they would be willing to keep a tally of what you were earning towards some imaginary sum for freedom. Even if you were paid directly, as far as the law was concerned you had no entitlement to property - every penny you earned belonged to the person who owned you in law. This meant that even if you were able to find ulterior ways of earning cash for yourself (as some were able to), you couldn't exactly waltz up to your master and expect him to take it well.
And this lack of legal identity also meant that there was no intrinsic right to purchase freedom for yourself. It was entirely up to your owner to decide whether or not they wanted to let you even try to work towards earning your freedom by purchasing it; if they said no, then that was the end of that. Even if they said yes, you would have to accept the possibility that the price they insisted on might simply be too high to reach: slaves were a high-value commodity. And even if you could raise the funds to buy your own freedom with the permission of your owner, this did not mean that your owner would let you - or that you could afford to - also buy the freedom of spouses, children, parents, siblings or friends (I've just written an answer about the historical accuracy of Roots that talks quite heavily about the importance of family to African Americans in slavery that might be of interest on this point). There was also absolutely nothing stopping the slave owner changing their mind, or moving the goal post of the cost of purchase to make it impossible to achieve. The obstacles to securing freedom through purchase were significant and dramatic - for most people it simply wasn't something they could ever realistically achieve.
But what if you could achieve it, or if you were liberated any another means?
Well, it depends entirely on the location and time period that you're talking about. The general principle is that a formerly enslaved person would have required some kind of written documentation - often called 'freedom papers' - to prove that they were in fact entitled to be free. The most formal versions of these documents would generally take the form of a legal deed, where the legal owner of the enslaved person would certify their soundness of mind and intent to liberate the enslaved person, and have this witnessed by a competent legal official. Very often these papers would contain a physical description of what the beneficiary looked like at the time of liberation, with the intention that anyone inspecting the papers should be able to verify their identity by comparing their appearance to the description on the deed. There were variations of these documents depending on the reason for manumission, and the requirements (formal or traditional) of individual jurisdictions. You can see an example of what a very elaborate version of what one of these documents looked like here, showcasing the example of someone who had their freedom purchased by another person (there are more examples in the sidebar).
But the obstacles to getting these papers and having them recognised could be considerable for most of slavery's history. When racial slavery was thoroughly institutionalised across North America, the white elite were always extremely concerned about the prospect of a large population of free black people developing. The presence of a sizeable number of free African American and African Caribbean people was seen by enslavers across the New World as a monumental threat to the stability and social order of white, slave-owning society - both because of deeply-held racial prejudices and out of fear that free black people might inspire enslaved people to try and forcefully secure their freedom. So across North America, we see different governments - colonial and state alike - trying to find ways to inhibit the growth of the free black population by tightly regulating the ability of individual owners to free enslaved people at will. This is one of the other tensions in slavery's construction: although enslaved people were supposed to the property of their owners to do with largely as they pleased, governments were also keen to interfere with the ability of slave owners to manumit people for the sake of preserving the racial order.