Some people pick up the radio without any problems and others have a really hard time with it. There is no easy answer, but by the time you finish your license, you will feel much better about it.
As for picking up when someone is calling you, that comes when you are not so focused on just trying to keep the airplane level and going in one direction. You will learn through practice when its time to keep a sharp ear to the radio. And dont worry about it. If I got docked for every radio call I missed second (third) time around, I'd owe my company money!
The other thing is that what the guys on a busy Tower frequency are saying may not make sense to you until you get into your instrument flying, because its different terminology.
Also, learn to speak properly on the radio first. Its OK to listen to something like LiveATC, or a scanner, but realize that the guys and gals on there may not always be using proper terminology, and I know from experience that a new pilot can pick up on something small (calling out "leaving 12.5 for 4" when descending) and think thats the "proper" way of doing things - at the end of the day, it'll be your hand thats slapped for incorrect radio use, not theirs!