It's a simple question with a complicated answer.
The basic problem is that the quieter your source--bird song, for instance--the more you will hear electronic noise from your recording gear. So you need to first establish a budget and then do research with an emphasis on low noise in mics and preamps (or a recorder's built-in preamp).
And of course, there are specialists:
http://groups.yahoo.com/group/Naturerecording/It depends how fanatical you want to get about it, and you can go to very expensive lengths to eliminate a few decibels.
That said, I recorded a conversation outdoors with the built-in mics of my Sony PCM-M10 and the birds singing and wind in the trees came through very realistically. It can, if you want, be that simple.
One thing I strongly suggest for ambient recording is omnidirectional mics, like the ones built into the PCM-M10. If you're going to just use the built-ins in a recorder, many of those recorders use cardioid mics, which are directional and good for pointing at, say, an interview, but don't sound as realistic. The Tascam also has omni mics.
You can generally get better quality and far more flexibility with outboard microphones, of which there are approximately a zillion choices and price ranges. If you do get outboard mics, you would want high-sensitivity mics--not the low sensitivity ones many of us here use because concerts are so dang loud.
Anyway, set a budget first, and people here (and at that Nature Recording group) can help you make choices.