And if they were given trials, how unfair were they?
I'm going to answer this without trying to over-complicate it too much, because the answer is very complex, particularly in the US where the situation varies so much from state to state.
Slavery was an institution filled with inconsistencies and paradoxes; the application of the law to slaves was no exception. The administration of justice in relation to slavery was remarkably inconsistent. Generally speaking, there was little to no recognition of the civil rights of slaves; in one notable judgement in 1861, the Alabama Supreme Court dismissed the notion that slaves had any civil rights whatsoever; they had "no will which the law could recognize" (Creswell's Executors v. Walker). With criminal law though, the picture is much more complex.
The extent to which black slaves could be held liable for criminal action was a source of great debate to contemporaries, and the situation varied considerably. After-all, inanimate property cannot commit a crime; only a person with will and intent can. Thus a paradox developed in which slaves were seen entirely as property in civil law - slave codes and laws generally prohibited them even basic rights like marriage - but somewhat more like persons in criminal law. This was a major point of criticism for many anti-slavery agitators of the day; that slaves were treated as either people or property according to convenience.
Throughout the period of slavery in the US, regardless of what the law said should be the case, petty offences were generally dealt with by plantation owners and overseers. Plantation owners and overseers had considerable freedom to accuse, determine the guilt of and punish their slaves for offences. It was much more efficient (and effective for maintaining authority) for slave holders to administer justice themselves. Only when crimes were more serious, or extended beyond a plantation's boundaries, would the judicial system generally become involved. Relatively few slaves, particularly in the early period, ended up in high courts of justice.
Beyond the plantation, in the colonial and early post-revolutionary periods especially, the primary source of administering justice to slaves was the local magistracy. Magistrates and justices of the peace were local officials who enjoyed often considerable powers to enforce the law, and considerable discretion over how it should be enforced. Being local officials, sometimes the entire process of lodging a complaint, trying a slave and dispensing punishment could take only a few hours. They had the authority to dispense considerable corporal punishment. Magistrates were not required to be men of great legal minds, and the guidelines for dealing with slave cases were often vague; particularly in the colonial period it was not uncommon for magistrates to hear cases in their own homes with no counsel for the defence. As time developed, there is evidence that the quality of the magistracy did as well; by and large however, it remained in many ways an extension of the system of informal plantation justice.
For serious offences, slave cases would be heard by higher courts, often involving multiple justices. From the late eighteenth century onwards, trial by jury was increasingly seen as an important element of any fair judicial system in the US. As such, by the early nineteenth century, many southern states allowed jury trials for blacks for capital offences, and some for felony offences. There are records of lesser offences being tried by jury as well, though this was far less common. Jurors were always white without failing; in Tennesse, Alabama, North Carolina, South Carolina and Mississippi, rules and guidelines were drawn up in such a fashion that a majority of jurors would likely be slave owners. In many states measures we taken to establish the theoretical independence of jurors from the owner of the slave being tried. However, attempts to challenge the legitimacy of jurors or magistrates are extremely rare except for in the final decade of slavery in the south.
As time went on, states began to extend more procedural rights to slaves tried for serious offences. By 1860 the vast majority of the US' slaves were theoretically entitled to considerable procedural rights in capital cases, including the right to appeal lower court decisions to at least one higher court. True procedural equality was difficult to enforce however, and was not construed in the interests of slaves - southern states pushed for better judicial rights as a way of demonstrating the fairness and legitimacy of slavery, rather than as a means of weakening the system of racial domination.
So the picture is really quite mixed. Yes, slaves could be tried for crimes, and as time went on efforts were made to make the judicial process fairer for them - but by and large plantation owners were responsible for their own discipline, and when recourse to the courts was required, there were considerable institutional and social obstacles for slaves. Judges and jurors alike were overwhelmingly pro-slavery in their mentality; whilst there were certainly occasions on which going to trial produced a favourable result for a slave, the judicial system of the period generally represented another means by which free whites maintained the system of white-on-black domination. Even the extension of the right of appeal served a pro-slavery agenda.
One thing I haven't commented on is just what exactly constitutes a crime. Regardless of the theoretical basis to the law in a state, across the US, slaves in practice lived under a very different law to whites. William Byrne's superb study of slave crime in Savannah 20 years or so ago found that the vast majority of crimes blacks were found guilty of were crimes against slavery and status; crimes that were only crimes if you were black, not white. In a bizarre contradiction, slaves were simultaneously held to be unfit for legal responsibilities like entering into contracts, but expected shoulder a much greater burden in criminal law. That distinction is always worth bearing in mind when considering this question - there can surely be no such thing as a fair trial for a crime against slavery, given the very nature of slavery as an institution.
If you're interested in this topic, I would thoroughly recommend Southern Slavery and the Law, 1619 - 1860 by Thomas D. Morris for a detailed but broad overview of the topic and Twice Condemned: Slaves and the Criminal Laws of Virginia, 1705 - 1865 by Philip J. Schwarz for a State-specific case study.
A few other useful sources: