A couple of quick tips before arm wrestling:
1. Don't arm wrestle more than once or twice every couple of weeks, because it puts a great deal of strain on your tendons and joints. The more you do it the more you'll notice you're losing to guys you should probably beat.
2. The right pschological attitude - So your smaller buddy has beaten you before. So what? Next time, after doing some arm training, psyche yourself up before you beat him. Use positive imagery in your head. Think about beating him, and how good it will feel after you do, over and over in your head. This positive visualization will only help come arm wrestling time. Also, you cannot let those previous losses even be a consideration anymore. You must believe there is no way you can lose. Look him straight in the eye before the match and tell him you've been working out and your arms feel 10 times as strong as they used to, and that you feel like you could "crush a coconut" with your "bare hands". It will give you a psychological advantage, and if you pump yourself up enough, you may feel as if you could in fact crush a coconut with your bare hands. Then, when you go to grip his hand before the match, make sure you grab a hold of his hand aggressively, and squeeze his hand with a much firmer grip than you have before. You should have a look in your eyes like you can't wait to get it on.
3. If you ever saw the cheezy Stallone movie "Over The Top", you might have picked up on the advantage to having your fingers over top of his during the match. Just before you are ready to begin, slowly run your fingers, one at a time (starting with your pointer finger) over his knuckles. You now have the advantage of coming from the top. It's psychological, as well as physical, because it gives you a leverage advantage.
4. One of the biggest mistakes in arm wrestling is trying to force your opponents arm to the side, this is a very unatural movement for the human arm, and leads to serious tendon injuries. As soon as the match begins, you should be pulling his arm towards your chest, more than to the side. If your fingers have been properly placed over his knuckles, this will be easy. Bring his arms a little to the side, but also towards you. What happens is your arm is now bent and in a very powerful arched lock. The more his arm comes towards you, the more straightened out his arm will be (extended towards you) and at that angle, it's nearly impossible for him to bi-cep curl his arm out of it, because you are on top and his arm is extended. Then you simply put all your force (and a little bit of your weight) down on his hand and flat on to the table.
5. After you've won, let his knuckles up from the table about an inch and then "accidently" slam them back down on the table for added effect. Tell him you'd love to do it again, any time he likes, because you know you can't lose anymore.
I haven't lost an arm wrestle since I was 16. I think I may have lost a friend or two because of the knuckle slam though, so maybe do that one at your own risk.