The best way to help in the Alpha is to take the surveys they have available from the Alpha Client itself. I don't remember exactly where it is, but it's somewhere on the home page of the client :)
Anytime you come across an issue it's always best to document it, or remember it very clearly so you can write a report about it using the survey function.
There is no real "board" for the alpha client, unlike the PBE, so try to use the surveys as often as possible if you can think of suggestions or perhaps come across a bug.
Bugs can also be reported in the "Report a Bug" board, so don't be afraid to post there if you run across an issue with the LCU.
Good luck! And thanks for helping out with testing the Alpha client! :D