I bench raw, but the principle's the same either way. First, your elbows are what provide support for the bar on the way down. You shouldn't be using your hands to manage the bar into place, but let your elbows act as the fulcrum to guide the bar down. Where your elbows end up is where the bar is going to be. So, when you bring the bar down, they should end up in a position that best supports the weight and be ready to drive the bar back up.
A shirted bencher may want to bring the bar down a bit lower than a raw bencher- that is more on his upper stomach than the top of his abs, though I'm not sure of the reasoning on this.
In any case, when they say tuck the elbow, it's really only a slight tuck Instead of flairing the elbows out, or hyper-extending them in (a sin I used to be guilty of when I first tried 'tucking them in') it should be a natural type of motion.
So you've taken the bar out, and let your elbows guide the bar on the correct path down. As they come down, you tuck them in by slightly rotating them in. It's a procedure that takes practise, your want them to end in a position to maximize your power: supporting the bar and ready to begin the drive up. Once the bar is halfway up, you begin rotating your elbows back out in order to support the bar into lockout.
When I warm-up, this is something I still practise with no weight on the bar. It's important to find that groove that's going to let all the component sof your bench to work together.