For audio recording there are two steps - the hardware/software to record and the software to improve/save.
Recording can be done on a variety of devices including dedicated equipment, cameras, phones etc. as discussed above. (I use my camera to record video and isolate the audio in the next step.)
Creating a good sound clip - one needs some software to make the clip really good and useful, especially if one records on non-dedicated devices in wind near a busy road. For this I wholeheartedly recommend Audacity (https://www.audacityteam.org/). It is free, open source and cross platform (on PCs (Mac, Win, Linux), not yet Android or iPhone).
It is super easy to use, and one can remove wind/traffic/camera noise, amplify, delete out unnecessary bits, and edit clips together. It can do a whole bunch of other stuff too which is not necessary for nature recording, but fun to play with should you be so inclined.
There is a good tutorial by an enthusiastic recorder of bird calls, Stein Ø. Nilsen - http://fuglesang-troms.no/audacity%20-%20a%20beginners%20guide.html