There are a couple of options available
self-emancipation. Run away from slavery either to a non-slave state or an isolated place in the South where you could live in an isolated community composed of other fugitives like yourself (parts of Florida and the great dismal swamp in VA/NC were noted locales for this).
Self Purchase. Earn enough money from work you did on your own time or via a contract with your slaveholder that guaranteed freedom after a certain amount of work that you'd done. Or in the case of legendary slave rebel, Denmark Vesey, you could win the lottery and buy your freedom.
military service. During the American revolution some enslaved people fled to British lines and joined the British military which guaranteed the freedom of many of these people. The US army also did that but to a far lesser degree
Extraordinary assistance. Occasional stories exist of enslaved people saving the lives of important or generous people through bravery and being granted freedom. Or they could give testimony (against other enslaved people most likely) and be given freedom by the state.
Manumission. Your slaveholder chooses for one of a host of reasons to give you your freedom. Or someone (or your church) purchases you to give you your freedom.