How do birds learn their tunes in isolation from their own species?
Birds have to learn their song patterns. 
They are able to chirp, but the songs with "meaning" are learned from their parents or whatever they learned to be their "parent".

Here is a paper that related bird song learning to human learning (of speech, for example). 
Birds brought up by parents from another species learned to sing their songs. 
There are many birds that learn to imitate other animals or sounds, so in isolation from all birds they will probably do this. 

I can't recall where, but I read a paper once, where little finches brought up by humans developed a song resembling the "Hello there, now there's food", their caretaker always greeted them with. (Not the speech, but the overall sound pattern.) They might not understand the signals, but they try to communicate nevertheless. Some birds use sound from other species to mock others, scare them off or lure them into thinking they might be more powerful than they are. 

Birds brought up in total isolation do sing, but not the typical songs you know from their species. Deaf birds who can't hear themselves, though, do not (always) sing.