GEAR
You can't make noise without distortion, so that's the most important thing. If you noise a clean (i.e. undistorted) guitar, it sounds like you just can't play, whereas if you fuck up a heavily fuzzed or overdriven axe, it sounds like you're doing it on purpose, thanks to the stirling work of Jimi Hendrix, Lou Reed, Neil Young and Sonic Youth, the big four feederbackers of history, who turned guitar noise into an art form.
I use a Marshall Shredmaster pedal and a Korg AX1000G  Signal Processor (or multi-FX, to everyone else). This is a pic of my setup.

Generally I use the modelling features of the Korg to get my sound; the pedal is turned off with the all the knobs turned up to full. All I have to do is hit the footswitch to turn on the pedal, and I get instant super-distortion and feedback which is constant, even if I stand a long way from the amp.
My guitar is a Fender-licensed Stratocaster copy called a Sunn 'Mustang'. It's made in India, which is unheard of, and is very rare but so cheap and crap that no one on the planet would ever collect it. It's covered on stickers and black tape to hide the hideous white paint job. I like cheap guitars because of the extreme low quality of the hardware; the pickups are so badly shielded that they feedback very easily, and have a really nasty, brash sound. Still, that's not to say I wouldn't prefer a 1965 Fender Jaguar.
I now have another guitar, which is good because I'd always wondered what playing in tune sounded like. I've repainted my strat in a Kurt Kobain pale blue, although I haven't scratched 'KURT 4 COURTNEY' in it, which is what he did. My new guitar is a Burns Marquee and is really, really good and not cheap at all.
My amplifier is similarly cheap. It has no effects except for an overdrive control, which was supposed to be connected to an external pedal, since lost. When the overdrive is turned up without the pedal plugged in, the amp goes crazy. The only problem with my amp is its small size, and resulting lack of bass response.
For cabling I use reasonably high-quality stuff, but I have one very cheap cable in the chain which, if whipped about violently, causes the amp to crackle.

FX
Effects are cool. My multi-FX unit does a pretty good job of 'digitally modelling' actual stomp boxes, but lacks the inherent coolness of them little metal units. However, stomp boxes need power, so if you have more than two or three, you'll need to either buy or construct a pedal rack to power all the boxes. The advantage of a multi-FX is that you have access to expensive FX without having to buy the pedal or boxes themselves. The main disadvantage is that unless you pay a reasonable amount for your multi-FX, it'll sound really really bad, and very inorganic and 80s. For the price range, I think my Korg is probably the best; the quality of some of the effects are on par with the $200-300 machines, although some of them do sound pretty dire, and not even in a good way.
BOSS make the best distortion pedals, value wise. Electro-Harmonix, however, are reissuing a lot of their 1970s range and these pedals and boxes are very reasonably priced, and probably the most popular make among good bands. The Big Muff distortion created the sound of American indie rock of the late 80s and 90s, along with the Pro-Co Turbo Rat, and both are priced reasonably.
The other alternative is very cheap and nasty boxes; cheap boxes have their own amusing properties and disfunctions. The only one I wouldn't recommend buying on the cheap is wah-wah; cheap pedals just don't work very well, and tend to sound very tame.

TEKNEEKS
The trick with noising is to make something that sounds interesting and difficult to achieve, rather than sounding like you meant to play something else, but just fucked it up. Here's a list of some of the most wacky techniques.
Slide. You can use a regular slide (basically a piece of metal the size of the third or fourth finger), or another household object, such as a drumstick, or, my personal favourite, a screwdriver. Slide up and down the strings to create an oscillating effect with is very Sonic Youth. Slide around the pickups to make some high-pitched shrieking.
Mute chords. Not technically noise per se, but one of my personal favourite guitar sounds. Lightly rest one of your fingers, usual first or second, over all the strings so that they don't move, but aren't touching any fret, then hit them with heavy distortion on and the amp on loud.
Bending. Everyone likes a bit of bending. A great way to make your guitar go completely out of tune. Push or pull a string up/down the fretboard, so it scrapes across the fret and goes up in pitch.
Tapping. Tap either the back of the neck, or around the pickups to make a rumbling noise or hollow jarring sounds. As used at the end of Sonic Youth's 'The Expressway to yr Skull'.
Screwing. Hmm, slightly misleading title; not actually making love to your guitar, but jamming a screwdriver blade between strings and fretboard and either sliding up and down, to doing other unpleasant things. If your guitar is worth money, or you've only got one set of strings, don't do this.
Feedback.Turning up your amp loud enough for the components and stuff to, er, react. Or something. Can be controlled by messing about the with amp, guitar and pedal controls. If you get it to the right pitch, you can make dogs howl for miles around.
Shredding. The process of playing the strings very fast to create a kind of messy tremolo effect. Also works rather well with an electric drill.
Detuning. If you guitar is enough out of tune, and distorted enough pretty much anything you play with sound like noise.
Pickup Switching. A little-used effect, partly because it relies on your guitar being extremely cheap, and making an audible noise when the pickup selector switch is flicked.

For more noisy noises, go to my Archive of Noise.
 

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