There are two commands you can use: /toggledownfall and /weather.
/toggledownfall is most likely what you're looking for – if it's raining, snowing, or storming it will change the weather to clear and sunny.
/weather [type] [seconds] gives you more precise control over the weather, but you have to give it more info. When you use it you set the weather to the specified type for the number of seconds you told it. The type can be either clear, rain, or thunder.
Since /toggledownfall is simpler and does the job – makes the rain go away – I almost never use /weather, but it's good to know both.
Both of these are only accessible if you have cheats enabled for your single player world (chosen when you made it) or are a server operator. If you're playing single player and don't have cheats on, you can turn them on temporarily: use the Open To LAN menu and make sure you choose cheats in the LAN options before starting the LAN game. Turning on cheats this way will only last until you quit the world and reopen it. (To more permanently turn on cheats you need a save editor like NBTedit.)