Most musicians use sheet music on stage, but for some reason rock/country/blues bands don't.
Here's what I do: I work on one song, with the music in front of me, and go all the way through. I don't let myself get distracted. I go all the way through to the end, even if I make a mistake I keep going. Then once I have that down, really down, so that I am bored, then I try to do the first verse without the music. Once I can do that, I add the second verse.
Basically, take your time, stick to one song, and play all the way through. Repetition is your friend.
Hope that helps.
Jon