Combat robots can be a fun hobby for all ages, but there can also be a danger of injury. Always have an adult help. Be safe! Use ear, eye, and hand protection.
Step 1 - The Rules
Get familiar with the rules of the event. Official rules can be found on the Robot Fighting League website, however the event organizer may change and adapt the rules to more fit the event. It is very important that you know and understand the rules for the event in which you want to compete. The best way to find out about events and competitions is by going to The Builder's Database.
Step 2 - How Heavy?
Decide what weight class you want to be in (the larger the robot the more cost and time involved.) A small 1lb antweight can still be just as fun as a big 240lb heavyweight (not to mention easier on the back.)
Step 3 - Choose your Weapon
Decide what type of weapon you want or if you even want a weapon.
Getting your weapon to be the most effective as possible will be key. It is a good idea to design, test, and build your weapon thoroughly before building the rest of the robot.
Step 4 - Find the Parts
You probably already have a design in mind, but finding the right parts is the key. There are several places you can get parts. Below are just a few:
Step 5 - Stay Updated and Communicate and Don't Give Up!
The Robot Fighting League forum on delphiforums.com is a good place to talk to other builders and get ideas or help. You can sign in as a guest or join if you like.
There are also a couple of books I would recommend by Chris Hannold.
The cost of a small robot will run from a few hundred dollars and the larger robots will run a few thousand dollars and up.
For detailed information on bot building check out the RioBots Tutorial.