This is a list of things that you will need for a fulling functioning studio. Listed in the best order I can figure out. Many people will stress something like room treatment being one of the most important things but I rather make music in a less than perfect environment than not make it at all.
01) Computer or D.A.W. (digital audio workstation)
02) Recording Software (this makes your computer a DAW)
03) Studio Audio Interface (also know as a soundcard and must have an ASIO driver)
04) Studio Monitors (the speakers you use for playback and mixing)
05) Midi keyboard (it is difficult to make tracks without one if there is any programming)
06) Mic Preamp (it is REQUIRED for any recording with a mic and many have d.i. inputs for recording instruments directly)
07) Mic (condenser mics require phantom power from the mic pre)
08) Cables (to connect it all) this could be between 3 and 4 because otherwise 4 would be little use.
How much you need of each item will depend on your needs.