I've been struggling with this for a long time -- and I admit it's probably because until lately, I never cared -- but how does one go about learning to properly mute strings as you play?

Even at low speeds, my piece of shit guitar loves to make all sorts of fun noises (sometimes I think even wind rushing past it makes it ring out), so while playing at a decent clip I find it extremely difficult to even comprehend being able to properly mute unneeded strings as I play.

But, a great guitarist has control of this... so I must learn. Any suggestions or tips to start with, or links to exercises, etc?

I appreciate any help you can give.

Palm mute the low strings while you play the high ones. Not a normal musical palm mute; actually rest your palm on them. Mute the high strings with the fingers on your picking hand, resting them between strings. When not using the index finger on your fretting hand barre it across the strings. And if you do a lot of crazy fast shredding or two-hand tapping just put a scrungy around the strings right below the nut, or order MAB's string mute. Obviously doing all of this means you have to spent a lot of time playing scales and leads really slowly until you get good at it.
Well first off you have to make sure your entire hand and arm position are properly adjusted, this is usually what keeps people from palm muting. You arm should be placed at the upper back of your guitar (still on the front if that sound confusing) and the bottom of your palm should be against the bridge right where the string meets the bridge. You can move you palm further onto the strings or further off the strings until you get a sound you like. Just play some scales until you think you got it. Once you think your there play a song that requires a lot of palm muting, some thrash metal like Megadeth would be a good start.

Your muting will more than likely sound pretty bad a first, and you probably wont be able to mute all 6 string effectively, but just like any other technique you can improve it over time.
Thanks for the responses, guys. I'm fine at muting strings when I choose to or when it calls for it in the song -- granted it's not always perfect but I can get the sound I'm looking for -- I just, for the life of me, can never play fast, clean melodies with distortion. I've only got Overdrive on this amp, which doesn't help (it sounds like ass), but even still, I should be able to clean up a lot of this mess with my own technique.

I'll take into account what you both said and see if I can't improve.

If nothing else, I'll stick to clean playing, where it's not an issue. I no longer have any delusions about being a great shredder someday. Not that my Bluesy style has ever hinted at shredding anyway.
If your guitar is making harsh noises, turn the gain down.

Use a clean setting for EVERY technique you learn, as distortion covers mistakes very well (Mistakes that will definetely be noticed by other guitarists and anyone else without virgin ears)

I know turning off the gain can really make playing suck but I started out on heavy gain and now im usually on clean settings.

I found that when I learned I never really had to concentrate on the muting in itself, and nowadays if I try to sometimes the rythm is so complex that my brain cant keep up and it just fails. What Im saying is.

1. Turn off gain, practice fretting a note normally, then a dead note (lift finger off string VERY lightly to avoid extra noise, you have to find the biting point as every guitar is different .

2. Check your action, action that is too low can result in muted notes being half sounded.

3. Dont worry - after a while muting comes naturally. It is genuinly the only thing in guitaring that I can say this for.

4. Work on only rythm and chords for a while (mainly barre chords, just practice sounding them and then muting them)

5. If your also palm muting, make sure your palm is RIGHT AT THE BOTTOM of the string. I mean it, right at the bottom on your bridge, you get a louder and crunchier mute then.