I once had a program where you could actually draw the waveform freehand and play it back. It was pretty basic though (this was back in the Windows 98 days).
Subtractive synthesis – which I’m pretty sure is the kind used on the track you linked – does allow you to make sounds pretty much from scratch. It’s an interesting idea, though in practice most of what you can do with it doesn’t sound anything like any real-life instrument.
Well, if you’re like me, you’ll look at all those knobs and switches and buttons and not have a single clue what any of it means. 
I linked to the MiniMogue in particular because it’s one of the simpler ones.
You can work it out by playing around with it. You begin with the oscillators. There are three here. The first two are normal oscillators, and the third can be used either as a normal oscillator, or assigned some special functions. These three oscillators are the things that create all the sounds you’ll be hearing. You can choose different waveforms. Oscillators 1 & 2 have:
[ul]
[li]A sine wave – mellow and smooth sounding pure tone[/li][li]Two kinds of saw wave – sounds a bit like strings[/li][li]A triangle wave - sounds a bit like a piano[/li][li]A square wave – sounds a bit like woodwind instruments[/li][li]Errm, two other things (I dunno what the heck they’re supposed to be).[/li][/ul]
The idea of using two or more oscillators is you can blend them together to make more complex and interesting sounds. So, for example, you can have a sine wave and a saw wave mixed in together. You can also change to frequency of the oscillators (the range, frequency, and fine tuning controls). You can, if you like, have the second oscillator playing a note an octave above the first oscillator. Or you can just slightly detune the second oscillator to create a richer tone.
Moving along…
The second most important part of a synth are the contour controls (on the MiniMogue they’re in the “filter” section, under “loudness contour”). These controls set how the sound plays. The four controls are attack, decay, sustain, and release. But often in other synths they’re simply labeled ADSR. I’ll try to explain what these are about.
If you think about a musical note, it’s divided into two parts. First, there’s the initial burst of sound, which is called the transient. After that comes the body of the note, that gradually fades away to silence. The attack and decay controls are for the transient, the sustain and release controls are for the body of the note. They work the following way:
[ul]
[li]Attack: This controls how quickly the note builds up to full volume when you trigger it. High values gives you a slower attack that fades in gradually. Low values gives you a sudden, abrupt attack.[/li][li]Decay: This controls how long the transient part of the note lasts, before it becomes the body of the note. A short decay makes the note very percussive. A long decay will let the note swell in the beginning before it settles down – think of the sound a huge gong makes.[/li][li]Sustain: This controls how loud the body of the note is compared to the transient. Low values gives you an effect that sounds something like plucked strings. High values gives you a more organ-like sound.[/li][li]Release: This controls how long it takes for the note to fade out after you’ve finished playing it. Think of an instrument like a piano, where you can still hear the previous note ringing after you’ve played the next one.[/li][/ul]
What else is interesting?..
If you look at the bottom of the MiniMogue it’s got an “Arpeggiator” section. There’s actually two different effects here. If you press the first switch on the left, that puts it into arpeggio mode. The synth will just continually play whatever note you enter in a steady rhythm. There are several modes, for when you want to enter more than one note:
[ul]
[li]Up: Play the notes in order from lowest to highest[/li][li]Down: Play the notes in order from highest to lowest[/li][li]Random: Play the notes randomly out of order[/li][/ul]
There’s also a speed control, which lets you set how quickly the notes are playing.
The right hand section of the Arpeggiator panel is what any other program would call a “sequencer”. It’s a row of sixteen buttons in groups of four. You can use this to create rhythmic patterns of notes that play with just one press of the finger. I’m 99% sure that Tristan and Regan used something like this to create the bass-line in the track you linked.
So, anyway, that’s probably enough to get you started. Most synths will have the three things I mentioned: oscillators, contour controls, and arpeggiator/sequencers. Most synths also have low frequency oscillators and filters, but that’s starting to get complicated (which is to say, I’m not confident enough about those to try and explain them). All the other bits you’ll find on a synth are mostly effects, which you would use to further shape and mess with the sound. MiniMogue is pretty basic in this respect – it only has overdrive, delay, and chorus.
By the way, the track also has a lot of electronic drum stuff going on in it. And that’s another topic again. There are sequencers that specialize in making drum sounds.
