Followup question: How dangerous would it be to travel long distance in the midst of the Revolutionary War?

The average Briton overseas had a few ways to ensure the transfer of mail from one portion of the Empire to another. The first and perhaps easiest of these was simply asking a friend or an acquaintance heading to your letter's destination to kindly drop off a letter for the recipient at a tavern or other structure serving as an ad-hoc post office if not at the recipient's house itself. Letters of the latter type might also have come with a letter of introduction, thereby providing an incentive for the recipient to entertain or otherwise reward the intermediary with a meal or company in the colony. This sort of informal postage was commonplace, especially in coastal towns and cities that saw a great deal of maritime activity. It was therefore entirely feasible for Alexander Hamilton to write his father from his childhood sojourn on Nevis in the 1760s and, later, for Hamilton to write his father with increasing urgency over the matter of reuniting father and son in the nascent United States. (This never came to pass.)

An alternative way to have sent your letters would have been through the British Army and Royal Navy's postal system, but this was highly dependent on your circumstances. The army's internal postal system was sometimes farmed out to professionals such as the Princes of Thurn und Taxis, who operated a postal system similar to that of FedEx today, but this would typically only last for the duration of a single campaign. Recipients of mail in the Royal Navy were at a much greater advantage over their land-based contemporaries due to the existence of the Admiralty's packet service, which became of increasing importance as they were also charged with carrying international letters and parcels for both HM Government and the general public.

Neither of these services would have been much use to a farmer in Massachusetts corresponding with another farmer in Connecticut. For land-based inter-colonial trade, the Thirteen Colonies depended heavily upon an independent system of postage run by colonial charter that was invariably rather expensive. Like most postal services of the time, letters were actually paid for by the recipient rather than by the sender and were, even more frustratingly, charged by the size of the letter and the number of pages contained therein. As a consequence, numerous letters were never paid for because the recipient simply could not afford the cost of postage. This wasn't due to a lack of American colonial infrastructure, but rather the fault of greed: postal contracts in both Britain and her colonies were seen as profitable enterprises rather than state utilities until well into the 19th century. Even in the metropole, a letter sent from Edinburgh or Dublin to London could start at about 1d (a shilling), or something approximating £10 today, meaning that rates for parcels would have been gutwrenchingly enormous. For a few lucky few living in London, however, there was finally the penny post where, for the cost of only a single penny, a Londoner could send a basic small letter to another Londoner living within a few miles of a post office. These offices were revolutionary in that they also required senders to pre-pay for letters sent to recipients, but disputes over the revenues of this service caused it to sputter in and out of existence over the course of the 18th century.

Now that you have a general understanding of how to send a letter, you may be curious on how to receive it. The crux of the early post depended on some investigative work as addresses weren't commonplace until the 20th century. Even today in much of the Commonwealth, addresses for grand houses simply take the following format:

Awesome Big House

Township p057 c0d3

United Kingdom

Major buildings have a similar format too. While Bute House in Edinburgh is located at 5-6 Charlotte Square, official correspondence of the Scottish Executive is simply given in the following format:

Bute House

Scottish Executive

Edinburgh EH2 4DR

United Kingdom

While modern postmen might have an easier time finding addresses today due to the advent of mobile phones, they still struggle to deliver postage to uncertain recipients in towns that may be so small or obscure that direct identification is impossible. In cases such as this, a postman would simply ask around and do a bit of sleuthing to discover the location of the recipient -- interestingly enough the Royal Mail continues to practice this today and has an entire team of detectives who attempt to track down unknown recipients with what is apparently some great success.

Yet at the end of the day, Britain's American possessions were scarcely populated and often tight-knit. A postman or friend would simply ask some local townspeople where the recipient could be found and would deliver the letter to them in exchange for payment. Assuming you were a fairly prosperous farmer or merchant -- you can read and write after all in this scenario -- it would be easy to locate you even if your friend wrote you from Bermuda.

You’d have found a house in a strange town by asking around. In short, it’s extremely unlikely that any houses in the American colonies ever had numbers.

House numbers had been introduced in some large European cities in the 18th century for various reasons of taxation and government administration: in various towns in Prussia in 1737, in Madrid circa 1750, in Trieste in 1754, in Paris (by a directory publisher) in 1779. London’s regulations on house-numbering date from the 1760s; Vienna’s scheme from the 1770s. Numbering was often done to aid the billeting of soldiers, and there is some evidence that British troops gave numbers to New York houses during the Revolution. It seems likely that these were soon removed by resentful property owners. However, this webpage from the New York Public Library indicates that New York and Philadelphia both had houses numbered by 1785, so New Yorkers may well have found the numbers useful, rather than merely unwelcome reminders of an occupying army.

The modern scheme that we know, of even numbers on one side and odd on the other, and of numbering based on a distance-based scheme rather than mere ordinals, both appear to have originated in Philadelphia in time for the 1790 Census. The logical technique of having house numbers relate to numbered streets—2801 being on the corner of 28th Street—also originated in Philadelphia in 1856 and was still called the “Philadelphia system” when Chicago switched to it in 1879. (Manhattan and San Francisco never adopted such schemes.)

Literature on house-numbering is scarce, but there’s a good bibliographic section on a webpage called The Gallery of House Numbers. Alas, most of the academic papers there cited are behind academic publisher paywalls, but you can read this useful historical review by Reuben Rose-Redwood of the University of Victoria.