I have a SteelSeries QcK mousepad (cloth), and I've notice that it's been getting dirtier and dirtier from regular use. What would be the best way to clean this using common household cleaning supplies?
First, I'd say figure out what the manufacturer recommends, and make sure you're not doing something to void your warranty.
Since it's cloth, and likely much of the crud is oil-based from your skin, I'd recommend a mild detergent, like what you'd use in the washing machine. Get it wet and rub a tiny bit of detergent into it, then rinse thoroughly and set on a rack or hang to dry. If you're concerned about damaging it, use a detergent designed for gentle cycles. Woolite is a brand that's pretty commonly available in the US, but it will probably vary wherever you are.