Acting is different from every other career in the game in that you don't have set days or times to work. To take a gig, go to the jobs panel of the Interface, then click the small button that reads Open Auditions. Alternatively, you can wait for your talent agency to offer you one, but you may be waiting a while unless you're with AI Staffing Agency.
You'll be presented of a list of roles, their pay, and any necessary Skills. The skills are mainly suggestions; at low level, you'll likely earn the audition regardless of any lack of skills, but they'll be more important for the actual performance. The audition listing also shows the range of pay for taking the gig, which will be based on your performance. If you're confident in your Sim's skills and you plan on helping them out, take whichever gig pays the best.
Auditions always take place the day after you accept them, but their time can vary. Be sure to check the jobs panel and try to work on the required skill or the Acting skill in the meantime. When the audition comes around, your Sim will automatically leave to take it and will return after a few hours.
Assuming they got the role, the job panel will update with when the gig takes place. Again, the time is randomized but will generally take place one or two days after the audition. You'll also be presented with the list of daily tasks that you can choose to do prior to the gig. Successfully doing them will boost your performance and payout once the gig itself happens.
When it's time for the gig, a pop-up will ask if you want to join your Sim or send them alone. If you're playing with a family, all the other Sims will go on free will off-camera until you're done. Following a Sim will help them though, so it's recommended to do so.
Once you arrive to the gig, you'll get a list of tasks to perform in the top-left corner. The time limit will be a little tight, so you won't have time to socialize too much during the event unless it's required in your task list. Note that after the gig you can hang around the lot for a while, so if you're trying to socialize for pleasure, wait until after the gig is over.
The main task to watch out for is Tell Director You're Ready to Perform. When you do this, all other tasks will cancel. Therefore, if you just immediately perform, you'll miss a lot of tasks that could have helped your rating. Do all tasks before telling the director you're ready.
Once you are indeed ready, the task list will be replaced by specific actions you need to perform on stage. Look for any glowing X marks on the floor to see where to perform the action. When you choose one, you can choose a Safe Performance or a Risky Performance.
