There are, or should I say, were three ways:
Sign in to beta (Unavailable).
Get a code from someone who got Beta codes and is willing to share one (Don’t buy them! Why you should pay when someone have these for free).
Follow TeamSpeak on facebook and twitter and count on your luck (Codes are one-time use so you need to be fast!).
Additionally, if you signed for beta and haven’t received your codes, you should contact Support.