General tips regarding stand-up (I also used to be a co-teacher at an improv comedy class):
- Don't expect to be able to "wing it" or to just have a piece of paper with topics to be funny about. Being funny on the spot and under the spotlight is tremendously mind-blanking. Have prepared material. Measure the time each joke (and additional spin-off follow-up jokes) takes, write it down next to the joke itself (I usually just write the punchline, but long or non sequitur set-ups might need to be written down too), and try to have three times as much material as you'll need--if it's a ten minute gig, come with thirty minutes worth of material, and spend the first couple minutes getting a feel of what your audience finds funny, so you can pick the most effective parts of your material.
- Have at least 2-3 "safety" jokes--cheap, simple humor, preferably with longer set-ups. They will be your go-to place if your audience isn't warming up very well at all, and will drag you out of the mud if a joke suddenly silences the room awkwardly.
- If your material isn't hitting home and your safety jokes don't seem to help, rely on the audience. Mocking the audience--hecklers in particular--is sometimes extremely effective. Try not to be racist (though it can work with the right audience), but cheap shots like uglyness, poor fashion sense, bad hairdos or body weight are all very popular. Don't forget to mock yourself as well--exaggerate when you do, people love hyperbolic humor. "I'm not saying you are fat, but the people around you need to be careful, (pause, serious look) I see some loose change starting to orbit your waist (raising your voice as you yelp out the punchline)"
- Finally, if everything else goes wrong, just talk trash about yourself about your miserable comedic skills ("I'm so bad at this, I got invited to perform for terminally ill children--as a form of euthanasia. Twenty two toddlers hung themselves in fifteen minutes").
Be creative, controversial, sporadically vulgar, and most of all, be confident. Dominate any nervousness, and if you find yourself feeling anxious, don't dwell on the sensation, tell the audience right away and make a series of jokes about it, until you loosen up yourself and your audience.
Best of luck! Live performing can be quite addictive, I hope you enjoy yourself.
As far as checking if your jokes are funny, as others have said, the funny is in the delivery. A good comedian can make you gasp for air after laughing like a maniac for minutes nonstop, using a list of old, cliche, barely amusing jokes. A bad comedian may have stolen world-class material from a better comedian and deliver it so awkwardly and with such poor timing no one even so much as smirks.