Bought an Apple Watch off of craigslist. Don’t know the previous owners Apple ID. How do I get into my Apple Watch?

Without the cooperation of the previous owner, you have no option which will allow you to use the watch.

Read: Turn off Find My iPhone Activation Lock - Apple Support for the details.

You don't. You need the previous owner to unlock the device. I don't think that Craig's List has any alternatives for you. You just wasted however much money was spent. Sorry for your loss, but as long as the previous owner is logged in and has the device Activation Locked, it is still their device.