Basically, play the game and note whenever something goes wrong.
It is best if you can explain
"what went wrong" (what needs improvement)
"When and where it went wrong" (How to see what needs improvement)
"How do you reproduce it? if possible" (Why it needs to be improved)
If you can provide answers to these questions (and do so) you are likely a good beta tester. Often it is best to explain "what went wrong?" with information that includes screenshots, videos, or crashdumps, in the case that words are not enough to give a bug or glitch justice.
Having the ability to communicate through text and the drive to do so is obviously important. If many people give bugs they discover with the above questions (or provide feedback with the questions in brackets) then the public beta should contribute very well to the final product.
An example of a BAD piece of feedback would be:
"I think the matchmaking system sucks. It needs to be better"
an example of a GOOD piece of feedback would be:
"I find waiting for matches to be very long and boring. I don't think my attention span lasts for over 5 min, and if that is required to find a match, then at least provide some sort of noise or queue to let me be aware a match was found since I am unlikely to still be watching my screen after 5 min.
Another thing I noticed was that often when it does find a match, a player drops almost every time, and the teams end up being unbalanced. I know I'm behind a Linksys router with Cox as my ISP and my connection is generally pretty stable, but I wanted to share my information to help narrow down where an issue my exist."
(or at least I imagine that is good feedback. I think a dev could provide better clarification)