Basic Strategy
Start by choosing a rock, then move on to paper. Then, scissors are the way to go. Unless, of course, you're playing against a robot, in which case, you should just give up.
Advanced Strategy
For the truly experienced player, the key is to create a rock-paper-scissors cycle. Start with rock, then paper, then scissors, then rock, then paper, then scissors. Repeat this cycle until your opponent gets tired of playing.
Counter-Strategies
For those who want to be the odd one out, the counter-strategy is to play all three moves randomly. This will either confuse your opponent or make them think you're crazy. Either way, it's a win-win.