I'm one of the few members of the club who had to auditon in an open mic. Due to the increasing popularity of the club, open mics are now the method used to become a member. Here are some of the things that brought me success.
1. Try out your material before getting on stage.
I feel like I have a pretty good feel for what is going to be funny, but I would never get on stage in front of a large audience without running my jokes by some friends first. No, your parents, 4 year old sibling, and significant other don't count, they will laugh at everything you say. At the last open mic it was clear that some comedians had not done this.
2. Break out of the BYU cliches
Whenever I hear someone start a joke with; "One time I had this craaaaaaazy companion," or "What's the deal with church/sacrament meeting/something Mormon," they tend to lose my interest. Of course you have to know your audience, and at times I have told jokes on these topics. But you have to consider that if you are telling a joke about one of these topics there is a good chance some variation of it has been done before, so it'd better be unique and very funny.
Even when I'm telling jokes about things on campus, I form them in a way that I could potentially replace a few words and tell them to a non-BYU audience.
3. Watch some stand-up or read about how to write jokes
This point can best be explained with a TRUE story. The other day I was at a party, and some guy came up to me and said that he wants to try out for Humor U. I asked him if I could hear some of his stuff. He proceeded to tell me a joke that included his life story, various mathematical equations, and a commentary on some political issue, then he ended with a corny and irrelevant punch line like; "that's why you should never put a fork in an electrical outlet kids!"
I'm no expert, in fact I'm pretty new to stand up, but a joke should have a short set up and then a punch line that actually has something to do with the topic. Watch some stuff on youtube and practice your delivery before an open mic.
I'll end with a little on how my experience went. There were around 20 comics who auditioned. I did my 3 minute set, and it killed. A few of my friends were there, and one of them told me that as he was leaving he overheard people saying; "Man, that black dude was hilarious! He could really tell jokes!" I was the only black dude who tried out, so I assume it was me they were talking about, haha. I don't want to come across as prideful, because frankly I'm pretty new at all this. But if you do all of the above you will probably do well. The next open mic is September 16th. Good luck!