Grab a fake book and start digesting them!
"Fake books" were historically completely illegal compilations of lead sheets (containing chord changes and melody lines) used by musicians as a quick reference for any one of the hundreds of charts they'd never seen before. These were completely illegal because no one was paying to license these songs from the original composers, and you could see upwards of 1000 charts in the same book. Being illegal bootlegs, the quality and accuracy of the notation was always suspect, and it took decades before Hal Leonard and other legit publishers got their act together and went through the arduous task of licensing every chart and publishing their own compilations.
A "real book" is another term for the same thing -- the original real books were no more legal than the first fake books, but they were ostensibly more accurate, and those particular books became very popular.
Certain books are specifically geared towards vocalists, and include lyrics, but most do not.
The underground culture of fake books continues to this day -- even though there are now many legally published books like the one linked above (and related items), illegal PDFs can be obtained through shadier channels.
You will learn how to create your own lead sheets by understanding existing ones -- this is a basic literacy process that applies to any kind of language acquisition. Probably the most challenging aspect of lead sheets is chord symbol notation. There are many different "dialects", but at the end of the day you will gain the best understanding by listening to recordings and matching your ears up with your fingers, and finally both up with your eyes (the symbol on the page).
Some other helpful resources for understanding chord symbols are actually available for free from Jamey Aebersold's website. The Aebersold series is another incredibly useful source of lead sheets -- each of the 100+ volumes of play-a-long books comes with a CD recorded by a professional rhythm section.
The only apps I'll mention are my favorite score reader, into which you could load any lead sheet PDFs you have, and iReal b, which doesn't contain any melodies for copyright reasons, but can be used as a "Band-in-a-Box" (competing software), to generate rhythm section accompaniment for any set of chord changes. (Chords are not limited by the same copyrights as melodies, so iReal b is able to distribute a package of 1000 songs' chords from their website for use with their software.)