Character sketches and character profiles are often confused for one another. The best way to tell the two of them apart is to see the profile as more like a questionnaire that has been filled out by the character about themselves. A sketch, on the other hand, is more like a scene revolving around the character: how they view the world, how they view themselves, how they believe the world views them. This sounds rather complicated for a single scene, doesn’t it? Let me break it down.
Focus on one world issue. Sexism, racism, ageism, etc are all issues that are current and good to start with. But perhaps you are set in a different time or in a fantasy or science fiction world. Do these issues still apply or is there some other point of contention that has your characters split? In that case go with whatever applies to your world and your characters. If you don’t have all of that sorted out, then go with something current. Trying to find something that your character is opinionated about—or strangely not—can be a difficult task, but once you have a controversial issue to write about, the character sketch comes rather easily.
The next aspect you need to take a look at is the setting of the character sketch. Remember, you’re actually writing a scene here, so where they are is key. Don’t spend all your time worldbuilding, as that would be a waste (unless you really need to flesh out the world your character lives in). Right now you’re concentrating on your character and their point of view. You can choose action—your character is running from something or someone, you can choose dialogue—talking to someone they have a conflict with is a great way to represent your character’s view, you can choose to have a benign scene where they watch something happen to someone else as well. The sky is the limits as far as setting is concerned, but make sure it counts for something.
This can be in answer to a challenge: using a specific word in your sketch, writing a certain amount of words, etc. Explore your character through this one scene, see what it is about your character that you might not know. Like whether or not they are brave, whether they keep a level head in stressful situations, if they think ahead. All of these can be pulled from many situations and can be shown multiple ways. Don’t be afraid to write something out of the box!
Filling out questionnaires about your character may fulfill the same need, but in order to do that you need to ask the right questions. This can be insightful, certainly, but sketches are like taking an adventure in someone else’s shoes.