How are portraits used?
The portrait is used in the chat window--both for messages "spoken" as that character, as well as in the lower part of the chat panel, where you select the character you're speaking as. The portrait is also used for the character token if you haven't selected a separate image for the token.
How to set the portrait image
Go to the character editor. (See "Editing a character".) Once in the character editor, just click on the character portrait and you'll be prompted to select an image from disk to use as your portrait. The image is automatically transferred to any participants who don't already have it.
Tips for choosing a portrait image
In general, you want a portrait that's square (width and height are equal). Otherwise, you'll have empty space either top and bottom or right and left, when it's used as a portrait, and it will look odd if it's turned into a character token on a map, because those are forced into the shape of a square grid on the map. You probably want to constrain yourself to 300x300 or less. This gives you enough resolution for a decent looking portrait, even if it's zoomed considerably, and yet it's small enough to not consume a lot of memory. Using a large image for a portrait is very inefficient, because they're almost never used full-size. Finally, I like to use headshots for portraits. They look better in a square shape. Usually portraits (and portraits used as tokens) are too small to really see the character well if you use a full body shot. There's definitely a place for larger, full body shots of characters, but I'd recommend that you use a handout for that, or put image objects on a separate tabletop.