This is a bit tedious to set up, but it should work:
Put the camera on a tripod.
Place a stool or chair or a broom or really almost anything where you will want to be in the photo.
Focus the camera on that object.
After you have focused, switch the camera to manual focus so that it won't change where it's focused.
Set the camera to use a self-timer. You'll probably want at least 10 seconds.
If you're comfortable with manual exposure settings, use the smallest aperture (larger f-numbers like f/5.6 or f/8) that you can get away with. This will put more in focus which will give you a greater margin of error. (It also helps that your compact camera will have a larger depth of field compared to, say, a DSLR). Using a flash will let you use a smaller aperture also.
Remove the object that you focused on, but mark on the floor where it was. The idea is that you've focused the camera at a certain distance, and you're going to place yourself there.
Well I'm thinking the point and shoot will have face detection in portrait mode so will automatically focus on your face. Because the sensor is so small you won't need to worry about depth of field having your nose in focus but not your eyes etc. It should be that simple... crosses fingers