The Continental Army and state forces relied heavily on volunteers lured by bounties, land grants, and patriotism. However, when quotas went unmet, states turned to drafts from the militia:
The Continental Congress (1778) urged states to draft men from their militias for one-year terms in the Continental Army.
Individual states passed laws for this. Examples include Connecticut (1777) detaching men for 10 months and Virginia calling for county levies.
Militias were often divided into "classes," with one or more men per class drafted by lot or rotation. Substitutes were commonly allowed (a drafted man could pay someone else to serve in his place).
It was very different than a draft.