DOTA 2 is in its closed beta phase. This means that you need a beta key to download and play it. The beta key is free and I highly discourage people to try to buy any from anyone besides the pack from the Dota 2 Store. Here is some info on how to get a key.
DOTA 2 Beta Key Activation Guide
(For those who already have Steam accounts, you can skip steps 1-2.)
1. Download Steam. http://store.steampowered.com/about/
2. Create an account and log-in.
3. Go to “Games” and select “Activate a Product on Steam”
4. Click “Next”.
5. Read the Subscriber Agreement and click “I Agree”.
6. Input your beta key code and click “Next”.
7. Click “Next”, after you click “Print Receipt” (Optional).
8. Make sure you have enough space for the game and click “Next”.
It will show you the disk space required, space available and estimated download time. The estimated download time is usually MUCH larger than it really is. When I had to reinstall my DOTA 2, it look me about 5-7 minutes to download the whole thing.
9. Click “Next” again and it will start downloading.
10. Wait for it to finish downloading and PLAY!