So you want to build a home studio. You can do it! Two important factors are what you want to use it for and how much you'd like to spend.
But let's start basic.
FIVE THINGS YOU NEED FOR A HOME STUDIO
1) A computer
2) Audio interface (this gets audio into your computer. In a pinch, you could use a portable recorder)
3) DAW software
5) A good mic or two
Oh, and piles of pillows or blankets to deaden the sound.