You will need DAW software to put on your computer. Your options depend on your budget - you could go for Pro Tools or Ableton Live, or a cheaper option like Garageband (if you have a Mac), or even a free program like MuLab from MuTools.com (which is still good despite it being free).
However, to run a DAW without too many problems, you may need a better computer. Your money will go further with a desktop compared to a laptop as well.
You'll need an audio interface. A great one to start off with is the Focusrite Scarlett 2i2. You can connect your speakers to it, and it'll connect to your computer via USB.
Do you want to make electronic music, or do you want to record real instruments? If you want to do the former, get a MIDI keyboard, like the Akai LPK25. If it's the latter, get a microphone with a mic stand. A good choice is the Shure SM58.
It can take time and money to build up even the most basic studio, so don't worry about getting everything all at once. Build it up over time.
The first thing I would recommend is a better computer and run MuLab on it. Look for lots of freeware on the internet. You can get loads of free effects plugins, synths etc.