Whole books have been written to answer your questions 🙂 Assuming you;re new to producing, here’s a 10,000 foot overview. The core of a home production system is a DAW (digital audio workstation), which is software that runs on a PC/Mac and provides what you need to record, mix, sample, etc – Ableton Live, Cubase, Pro Tools are examples of DAW software. Inside of your DAW is typically where you would run synths, effects, and other audio tools. These are usually called plugins, and typically come in VST (effects) and VSTi (instruments) formats. These can be controlled with MIDI keyboards (or any midi controller). You will probably want to add an audio interface, mic, and monitor speakers – here’s an article on lifehacker that covers some of the basics.
http://lifehacker.com/the-basics-of-music-production-lesson-1-set-up-your-h-499088482
As far as hardware requirements, no one answer – anything decent (PC or Mac) will suffice, but when you’re running lots of effect and instrument plugins, fast CPU counts.
TLDR – to get started, download an eval of Reaper, a good inexpensive DAW. Then, try out some free VST and VSTi plugins – here’s a good site to start with. This is some fairly complex stuff, expect to spend a lot of time reading and experimenting.
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