I did this on my Westwood T1200 which has a 12HP B&S, though they are mechanically the same engine...
Where the fuel pipe enters the engine, there will be the carborettor, which looks like a small metal bowl. there is a screw. Before continuing, make certain the the petrol is turned off or the tank is empty!!!! Undo this all the way out, but DON'T lose the spring. lots and lots of oil should pour out, so be ready to catch this. after it has stopped, send down a tiny bit of petrol to flush it out. then put the screw back in all the way hand tight; before unscrewing it 1 and 1/4 turns.
Your next job is to get the air filter out. This is above the carb in a silvery container with two screws. Undo these and take out the foam filter and paper filter together. Be very very carfull not to rip it!!! Now, get a bucket of hot soapy water, and rinse them out fully and carefully, before putting them on your boiler for a day or two.
While they are drying, drain all the oil from the engine and replace it with fresh oil. When the air filters are dry, put a little bit of fresh oil on the foam one and squeeze it in your hand so it is all covered. put them back together and screw the whole assembly back as one peice.
Now to see if it works! Turn on the petrol, wait a second, then crank it. If its a pull start, as mine is (the electric starting motor is shredded!), the it will take about four long hard pulls on full thottle but NO choke. If its electic start, then about 30-60 seconds on cranking. It should fire up un-willingly, before revving up. Just to warn you, it will smoke on hell of alot!! drive it around a bit till the engine is warm, and after about half an hour it will only smoke a little.
Hope this helps!
Aaron (15), December 2008