I have this vague notion that people can make pretty decent sounding electronic music on a common home computer, using free or cheap software.
Is this correct?
If so, what is it one needs to have, exactly?
Yes, it’s true. All you need is a computer and maybe some headphones. The main piece of software you need is a digital audio workstation (or DAW). If you google “Free DAW” you’ll find a bunch. (I should mention that I’m talking Windows based as opposed to Mac or Linux). Once you settle on a DAW, go hunting for free plugins - there’s tons out there. The most common plugins are “virtual studio technology” plugins, which come in two flavors - VSTs and VSTIs. VSTIs are instrument plugins and VSTs are audio processing effects like reverb, compression, pitch manipulation and so on. I’m sure you can find some half-decent VSTIs that do a reasonable job of making synth noises and electronic drums.
So that’s all you need - a DAW and a bunch of plugins, both of which can be had for free or for cheap. Of course once you have them you need to know how to sequence/program them so they make the noises you want them to.
I’m not an electronic music guy…I’m more old school musician (guitar/vocals). I use Reaper which is a popular inexpensive DAW. It may not be the best for doing electronic music but it’s certainly more than capable of being used for that purpose. I do program drum sequences and I also program keyboard parts, either from scratch or program corrections to my poor playing.
You can even add vocals. Google “Vocaloid”. There are several male and female voice synthesizer softwares. The most popular is Hatsune Miku. There are thousands of songs by her out there. She has been Japanese only but the first English language version of her will be released in a few days. HatsuneMiku - YouTube
You might want to look at a Tracker, of which there are some good free examples. They are often used for electronica.
I’m going to be completely honest with you. If you start up with a crappy, cheap DAW, it sound really dumb and you won’t have the control over the sound that you will want or need. Personally, I use FL Studio Producer edition and have made countless hiphop and electronic songs with just that. A lot of people like to use Ableton and some use Reason, but both are frankly kind of weird and have a steep learning curve for beginners.
Just get yourself a (totally not pirated) version of FL Studio, learn how to use the step sequencer, quickly realize you’re just supposed to make loops in the step sequencer and not entire songs, and then mess around with all the synthesizer presets for about 2 years until you make something worth listening to.
Sorry if this sounds cynical, I’m just basically describing the evolution of my production. 
EDIT: If you dare even think about picking up GarageBand I will hunt you down and kill you.
I’ve used FL Studio for a long time, but I don’t really do much anymore. I did this track with FL Studio using only isolated vocal tracks provided by the band (and one sample I got from another track by them). Everything else was created and sequenced in the program.
Well, if free is your primary criteria, it would be very difficult to beat Linux. Ardour is totally overkill for my multi-tracking needs, and free. It does have a steep learning curve, but any DAW worth using will.
However, I’m another person who usually is recording traditional instruments, rather than creating electronic music. For creating electronic music, you’ll probably want a synth, a drum machine, and a sequencer to tie it all together before you get to the DAW stage. Again, if you’re willing to deal with Linux, tracking down documentation, and a steep learning curve, this wiki page is a good place to start. If you are totally new to Linux, use the Ubuntu distribution as your starting point. It’s incredibly user-friendly, and most open source programs that are anywhere near ready for prime time are available as a precompiled package, so you wont have to learn how to compile source code to get almost any program that’s worth getting.
And don’t let anyone tell you that your music isn’t good because you didn’t pay enough to produce or record it. That’s the most laughable criteria that could exist of what constitutes good music.
I missed the edit, but I feel I need to add: When I say synthesizer, I don’t mean you go buy a Moog or a Casio keyboard, there are software synths available, that you can control in a variety of ways. For example, one of the synths on the wiki page above is controlled by using the mouse like a bow. :eek:
LMMS and Anvil Studio can do pretty good stuff.
Free! Free! Free!
Tutorials on Youtube.
Reason does indeed have a steep learning curve, but it can make some awesome sounds. Arranging is hard with it tho, IMO.
Fruity Loops is an easier learning curve, but still difficult to use for subtle changes (again: IMO).
Acid Pro is easy to use and has a lot of extended options available once you master the basics.
GarageBand is like Acid, but more difficult to do the advanced stuff.
Logic Pro is currently my software choice for recording and mixing, and I use the Ozone 5 plug-in for mastering. IMO, for the price they can’t be beat. I turn out recordings that sound as professional as anything sold in stores or played on tv/radio.
ETA: I don’t do electronica/techno/dance music anymore, but I’ll stand by my recommendations.
I work with a program called NoteWorthy Composer, which has MIDI sounds. So I guess you can make MIDI files with it, although that’s not what I use it for and I don’t know if that’s what the OP had in mind.
There’s a very basic browser-based application that you can get started with right now without having to install anything…and free of charge.
It is sort of similar to ReBirth (which I can’t believe is old enough to get a driver’s license). Also pretty easy to learn and you can get it making noise right off the bat…and also free.
I spent years looking for a good “Music Processor,” something that lets you stab notes down onto a staff. There are many, today, but twenty years ago, damn few. (I used the “Bank Street Music Writer” for the old Commodore! Ah, those were the days!)
Today, I pay a bit extra and keep up-to-date with the Mozart Virtuoso music processor, which is pretty nicely full-featured. But…pricey. There are lots and lots of nice ones for a bunch less money.