How does one get a DotA 2 beta key?

One does not simply,

Get a Dota 2 Beta key.

One has to fill this out. steam://takesurvey/1/

If you have a playdota account created before 2nd Feb, just enter the giveaway draw. Alternatively you can buy/trade games for it.

How dare you sir! HOW DARE YOU!

by offering various erotic massages

You can enter various contests on the internet. One of the biggest is the Playdota draw, they hand out 120 keys daily. I personally got mine when they had a huge wave of 5k keys over Christmas.

http://tinyurl.com/dota2survey

Have a friend who has a friend that works at valve and has tons of keys :D

Dat hardware survey.

Well besides the one i got from the playdota forums (hint: you should go check, i think they're still giving them away), i wouldnt be surprised if they start mass inviting in a short time, considering they're releasing the Dota test and are increasing the servers capacity, i see more people log in every day, so keep your hopes up :D

I got one in the christmas gift pile and i traded for 10 coal (not knowing what it was worth) cries

One simply gets a Dota 2 beta key.

No, seriously. Did you sign up for the beta? If you did, you'll more than likely get a key eventually.