A word of caution guys, be extremely careful if using a pressure washer (either hot or cold) to get the worst grime off, as it can weaken the structure of the tyre walls. This is particularly important for those tyres known to have issues with sidewall cracking/perishing, as an example I have major problems with Goodyear 7.50 x 16 Xtra Grips.
Tragically, I have to admit to liking my Landy being all clean and shiny (in fact I take a lot more care of the Landy than I do my everyday car), and tyres come into this. I use weak soapy water and a brush to get any dirt off, followed by a fresh water rinse, and once this has dried apply a coat of tyre dressing, or preferably tyre foam as mentioned by Phil P. I like the 'sparkly' look personally, but if you dont, just carry out this process a week or two before the event you want to attend, just to allow any sheen to die down.