The other poster suggested getting the Real Book, which is a good idea, but I'd go one step beyond that and get the iRealPro app. It has chord charts for basically every jazz standard and will transpose them for you in case you would ever need to play them with someone else in another key. It's kind of cheating, but it gets you there.

As far as tips on actually learning the tunes, try to pick up a bit of jazz theory -- there are plenty of good videos out there that will explain it in terms you can understand. The vast majority of jazz tunes are built from ii-V-I chord progressions in sequence. Once you learn to recognize those chords and their variations as sort of a single unit, you can have a much easier time memorizing a tune by just thinking something along the lines of: start out in C, then a ii-V-I to F, ii-V-I back to C.

Jazz is obviously a very deep subject and basically a language all on its own, but this might get you started.