When learning a new tune and playing it for the first time, it's highly recommended to identify the different sections and mark them accordingly. Standard song form of A for Verse(s), B for the Bridge is suggested. Not all tunes are put together in the same way, so mark what works for each tune. In this manner, you can get a overall view and understanding of how the song is constructed.
"I like people who have worked long and hard developing music through introspection and dedication." - Bill Evans
When practicing, isolate and break things down into smaller sections to allow specific focus. Practice each small section reduntandtly, over and over. Finally, when you have accomplished this throughout the tune, put it all together and start to practice the tune as a whole, as you would in a performance.
Practicing the performance of a tune in it's entirety is necessary to give the piece legs and to determine how this piece of music affects you, and in turn, how you wish to express it. Ignor the occasional wrong note. It is more important to play with continuity and symmetry from start to finish. Often it takes a long time to determine how you want to play the tune, and of course, that never remains quite the same.
"Master your instrument, master the music and then forget all that and just play." - Charlie Parker
When all the academic work is accomplished, now it's about putting yourself into the music. Find the feeling you get from playing this tune and bring it to life. Strive to play without thinking, only feel. Let the tune play itself. It is only through unconscious competence and spontaneity that we truly express ourselves honestly.
"Play what you feel, feel what you play." - D C DowDell