There’s very little literary material in the Aeolic dialects that has survived to the present – just fragments of the Lesbian poets Sappho and Alcaeus, which are mostly quotes transmitted by other ancient authors, as well as some scraps of papyrus, and one or two possibly complete short poems. The more important fragments, especially those of Sappho, are so tantalizing, and it’s crushingly sad that so much has been lost.
There are also plenty of inscriptions in local dialects that are classified as Aeolic (e.g., Theban Boeotian as well as Lesbian). I believe there may also be some Hellenistic poetry purportedly written in Aeolic several centuries after Sappho and Alcaeus, though I haven’t checked this.
There is a considerable Aeolic substrate in the language of the Homeric poems, but that language is an altogether unique conflation of forms and vocabulary from several dialects. If you are interested in the Aeolic/Lesbian poets, it would be helpful to have some Homer under your belt before you tackle them.
Ancient Greek choral poetry, including choruses in drama, is generally written in some form of a literary Doric dialect, not Aeolic.
Because there is so little material in Aeolic, there are no textbooks specifically teaching Aeolic Greek: you can simply learn a few characteristic differences from Attic/Ionic, and most of the fragmentary Lesbian texts require substantial commentary anyway. However, you’ll find discussions of the Aeolic dialects in grammars and other works dealing with ancient Greek in general and the dialects in particular.
So Attic is the basic dialect you should learn to start, and when you’ve more or less learned your Attic (not easy and there’s no quick way to learn it), you should be able to approach the fragments of the Lesbian poets, if that’s where your interest lies. There’s a volume of the new Loeb series of the Greek Lyric Poets devoted to Sappho and Alcaeus, with English translation on the facing page, which I think you would find very helpful.
https://www.amazon.com/Greek-Lyric-Alcaeus-Classical-Library/dp/0674991575/ref=sr_1_1?ie=UTF8&qid=1525141117&sr=8-1&keywords=loeb+greek+lyric&dpID=41hIn9aQhUL&preST=_SY291_BO1,204,203,200_QL40_&dpSrc=srch