Buy a Travel Card from Underground (Tube) stations after nine in the morning. Purchasing a Travel Card before nine costs almost double. This entitles you to unlimited travel on all London buses and Tube trains. If you are staying for a week or more, you might want to get an Oyster Card, which gives you cheaper travel for a week.
Find a bus stop. They are clearly marked and typically feature a shelter. Better still, find a bus stations, which will offer a wider range of destinations.
Look for your destination on the timetable. There will be a big post with all the numbers of buses on it, and underneath the numbers there will be a line pointing to where you are now and in which direction the bus will be going.
Check with the driver. Once you have worked out the number of the bus you need, verify with the driver when you board that it is traveling to your destination.
Remember that fare for the buses varies. If you have a Travel Card you do not have to pay extra. If you don't have a Travel Card, tell the driver your destination and he will charge the appropriate fare.
You must know when to get off the bus and that can be tricky. Sit in the upper level of a double decker bus, where it is easier to see where you are going. Look out for Tube stations and other landmarks near your destination. Or, if you can, sit near the bus driver and ask him to remind you when the bus approaches your stop.