How many times should I go to the gym per week? What should I do there?

snowangle
I'm 5'4" and 135 pounds. I want to lose fat in time for summer (and just in general). I went to the gym 3 times last week (Saturday, Sunday, and Tuesday) and I missed the last few days because I got sick. When I go to the gym, I always start with 20 minutes on the elliptical and then I just go do whatever looks appealing for the next 30 minutes or so. Usually it's various strength training exercises and sometimes I go on the stair climber.

As you can see, I don't really have a system. Help me out?
How many times should I go to the gym per week? What should I do there?
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