I want to buy a synth to get tones found in club music, etc.

Eg. the tone found in 'Flux' by Bloc Party.

Now am I right in saying that I can plug my guitar into a synth, and play that and alter the sound? Or does it have to be through a keyboard, because all the ones I have found so far seem to be keyboards...

To be honest, I'm not really sure what I need to be looking for, so any advice is welcome.

i thought it was something usually built into the guitar... I may be wrong though
Shred Head
All that theory my guitar teacher tries to drill into my head just gets buried under piles of porn and I never manage to apply any of it
some keyboard synths come with a vocoder or some type of input where you could actually plug in your guitar. You can alter the guitar's sound, but you'd have to use the keyboard to do it, and I think you're looking for an actual guitar synth which is a completely different thing.

You should just google "guitar synth" or search for it on guitarcenter.com or something.