First find a game to apply for, in this example, I'll be applying for Primal Carnage.

First enter in your name and email address, it's like all the other online forms that you've done a million times over.

Next list your PC specs, make sure to give them your CPU model, OS, RAM amount and type, GPU and hard drives.

They may want to know where you heard about the game, be sure to let them know, they want to know how their marketing is working, or isn't. Since I heard from my girlfriend, I told them that!

The company may ask why you want to play their game, was it dinosaurs? Was it flamethrowers? Or is it a lollipop welding maniac? Make sure you let them know in a way that they know you'll be happy to spend the time helping them test their game to destruction and report the bugs you find. Dedication is the key. For my response, I simply put: "AWESOMENESS"

They may have a community around their game and may want to know who you are in that community. Let them know, it may help to see how active you are. As previously put, they want to know how dedicated you are to helping them, they could ask how much time do you spend gaming, make sure to answer them with a fairly accurate answer. I put: "Every 2nd hour not spent sleeping"

Lastly, answer any queries or questions they might have, be sure to fully answer their questions. Here's an example:

What is your favorite platform? X-Box 360, Playstation 3, Wii, PC, Other? What previous beta/alpha testing experience do you have? What makes you a good candidate? Would you be willing to provide feedback about the games and report any bugs that you find?
And here's my response:

PC. I've beta tested a few games before, some good, some bad. I didn't realise I was applying for a job, what's the salary like? I'd be a great candidate as I can break things and then whine that it's not working. Yes, I would be willing.
Click apply/submit and wait to hear back from them!