Most improv starts by taking an audience suggestion. It is a way of proving that everything is made up1 and giving the improvisers some external inspiration. There are a few unspoken rules about getting suggestions, many of which are quite obvious. It never feels important enough to go over in class, but it’s quite glaring when these rules are violated.

Be confident and friendly. Good advice for all of improv, but especially at the top of a show. The audience needs to feel comfortable enough to speak up.
Repeat the suggestion to make sure everyone heard it.
Check with the players. Glance over and see if anyone’s making a face indicating they don’t like the suggestion.
Be specific in the prompt. Giving the audience a prompt with detail makes it easier for them to think of something. In a viral video, Billy Eichner asks someone on the street to “Name a woman,” and they are unable to. Open-ended questions are much harder to answer. If instead, he asked “Name a woman in politics” or “Name a woman you spoke to recently”, it would be much easier to answer. Instead of “Can I get a location?”, try “Can I get a location that you’ve been to today?” or “—a place you’ve always wanted to go?”
Get specific suggestions. In addition to the point above, try to get a specific suggestion to start the scene. If you ask for a relationship and the audience says “family,” this is usually too generic to inspire a scene. Suggestions like “half-sisters” or “grandparent/grandchild” are easier to use.
Don’t go for the audience members trying to be funny. They came to see funny people come up with funny scenes. If the suggestion itself is a punchline, it’s hard to build off of.
Go for the suggestion that delights you. This doesn’t refute the point above. The best suggestions have something that is earnestly delightful. They might even get a laugh from the audience, but the suggestion-giver wasn’t trying to tell a joke.
Don’t use the prompt itself. If you ask, “Can I get the title of your favorite album?” and the audience says “Rumours”, then the scene should be about rumors, not favorite albums. This one seems obvious, but it happens all the time.
You can use the suggestion however you want. The entire scene can be about the suggestion or it can just be mentioned at some point. Audiences don’t care about how the suggestion is incorporated. If you ask, “Can I get a location?” and the audience says “Mars”, you don’t need to be on Mars. You can be on Earth planning a mission to Mars; you can be talking about the astrology of Mars; you can probably get away with just eating a Mars Candy Bar.
Pay attention to how the prompt is worded. In the example above, if the prompt was, “Can I get a location for the scene to take place?”, then the scene must take place on Mars. If you’ve set up this expectation for the audience, they feel cheated if you don’t follow through.
If the suggestion doesn’t make sense, ask. Some of my favorite suggestions involve a follow-up question. An audience member says an obscure place, person, or thing, and it’s clear not everyone knows what that is. I’ll ask them to define it or tell us more. These interactions are always delightful, and it’s great seeing the improvisers play with this idea that might be brand new to them.
Beware of subverting the suggestion. If the suggestion is the planet, Mars, and you instead eat a Mars Candy Bar, this might get a laugh, but it is a denial. These types of laughs are frowned upon in scenes because they are not in the spirit of “yes, and.” Nevertheless, there is no rule saying you must “yes, and” the audience. (Sometimes, it’s very important to tell the audience, “no.”) Therefore, this kind of denial exists outside the scene, and it isn’t against the rules, per se. However, consider that the suggestions are a clue to what this audience cares about or what is on their mind. Using the suggestions in earnest might delight them more.
Don’t play the “we all interpreted it differently” game. One player initiates the “Mars” scene as an astronaut. Then another player walks on eating a Mars bar and says, “Oh no! I thought we were going to the Mars Candy Factory!” Another player, recognizing the game, enters saying, “I can’t wait to meet the Roman god of war!” This scene can get a couple of laughs, but it quickly gets old. The characters are so incompetent that it’s impossible to build a base reality where they can reasonably co-exist. This game usually arises because of the point above. Some player loves the Mars Bar pun so much that they force it into the scene even when their scene partner has initiated a scene on Mars. Don’t be that player.
You don’t have to take a suggestion at all. Though most improv starts with an audience suggestion, many great troupes and performers prefer not to.2 It’s not a required part of improv. If incorporating the suggestion feels more like checking a box than providing actual inspiration, you probably don’t need it. If you are going to take a suggestion, earnestly try to work with it.
Further Reading:
3 Tips for Using a Suggestion at the Top of an Improv Scene by Jimmy Carrane
Different ways to use a suggestion in a scene
Ask Fors on learnimprov.com
A list of prompts you can use
Lloydie James Lloyd’s article:
Actually, this doesn’t prove anything. Ask any magician. As a joke, I’ve always wanted to do a scripted show that begins with an audience suggestion. “Can I get a suggestion for a number between one and ten?… I heard, “two.” Alright, a fully improvised play when the lights come up…. Two households both alike in dignity…” (proceed to do the entirety of Romeo and Juliet)
TJ and Dave are the most prominent examples.