Step 1: Click the Download link that says "Download".
Step 2: Open the launcher and use any Username or Password desirable. It will not actually use them, but to keep track of your profiles. For example: If I type in "firstname.lastname@example.org" and it isn't a real gmail then it doesn't matter.
Step 3: Click "Play" and wait for the loading bar to load fully. Then begin playing Minecraft!
Step 4: If you have any questions watch the video, and feel free to leave a comment on it. Also visit the "Forums" to see if anyone else has your problem. Or go to "Troubleshooting" and see if your problem is already listed.