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xeno-canto is a great resource for bird recordings. I'd suggest downloading songs for the 20 or so most common birds you see and making a playlist for them. Play the songs without looking at the name, and see if you can guess it correctly. You can start adding extra songs once you get those first ones down.
The other thing that's good is to record songs you don't recognize and look them up at home. I use a relatively inexpensive Tascam recorder for this, but I'm guessing a phone would work too, it just might not be as good at picking up quiet sounds.
I've been working on a free Android app to download songs from xeno-canto and play them in a shuffled order to study. It's still pretty rough, but works for me. Larkwire looks good, but as far as I know, it only covers the U.S. and Canada.