Here's everything you need to know about the NFL Draft. does Day 3 of NFL Draft start? Time, how to watch, stream, TV channels. The second and third rounds of the NFL draft will take place on Friday night. The Browns selected Myles Garrett with the first pick in the. The NFL Draft is upon us, kicking off with the first round at 5 p.m. PT on Thursday evening. We break down all the details of TV coverage.