In my book The Singing Life of Birds, I included an appendix entitled “Techniques” (pp. 402-409). My opinions (and they are mostly opinions) on how to record bird sounds have not changed substantially since then, and I recommend reading those pages for an introduction, available here: How to record

Many other sources on the internet offer advice as well, such as the following two:

My favorite source for all good information on recordings birds is the Macaulay Library at Cornell University’s Laboratory of Ornithology, with Greg Budney as curator. Check out their Recording Workshop, offered every June in California’s Sierras. See also their information on “Audio Techniques” and “Audio Equipment.”  Also at the Lab of Ornithology is a mini-primer on “Capturing Natural Sounds: How to record birds for fun and science.”

An especially thorough site is provided by the Wildlife Sound Recording Society. The Society provides reviews of Equipment and also a mini-course on how to record in their “newcomers guide.”