For a 16 oz. takeout cup: With worsted weight yarn and a G hook, chain 30. Join into a ring and hdc into each chain. Increase 2 sts every other round (e.g. inc 1, hdc 12, inc 1, hdc rem), checking the fit every once in a while, working a plain round to tighten it up if necessary. I like a cozy about 6 rounds high. Stretchy yarns like wool need fewer increase rounds - increasing 2 sts every third round might do the trick. If you want it to fit lower, start with a shorter foundation chain. Please note that I'm using US crochet terms here; in UK terms the half double crochet (hdc) is called a half treble crochet (htc).
Modification: if the foundation chain is making the cozy too tight to get on to a cup easily, use a foundation hdc (also called 'chainless') instead (there's a great photo and video tutorial on Moogly: Foundation Half Double Crochet).
I gave one as a small thank-you gift to a barista who makes me awesome iced decaf soy dirty chai lattes (chai latte with a shot of espresso). Barista delighted, shows to a bunch of our co-workers, co-workers make many comments on it. I need to remember not to downplay my skills - sure, it's something I just whipped up with scrap yarn and an empty takeout cup...but I don't have to say that. I can just smile and say thank you.