For those familiar with ESPN's draft format, the mechanics of yahoo's format are different, at least on desktop. You will need to click on a player in the list, and then head to the top of the screen and click the blue button that says you want to draft the player. I don't know how the mobile app works and don't intend to find out.
For everyone, please turn on autodraft if you are leaving your device, even just for a couple of minutes. No one likes to sit through 90 seconds of nothing. Thank you.