As you probably found out, you played single draft. It'll give you an intelligence, strength, and agility hero to choose from. If you want to try all the heroes, uncheck that.
Also, there's a group http://www.escapistmagazine.com/groups/view/DotA-2
Anyway, I never really got nervous playing Dota like I did with Starcraft, or even LoL for some reason, except for when I queued for the very first game I played. Once the game started I mellowed out and just had fun.
Try playing with friends, or having music on. Maybe also watching Dota videos (like Purge's channel) if you can be bothered, since once you learn more about the game and know what's happening, you won't be as stressed.