How can you tell how many stars you have on mario kart wii?

After a grand prix, on the results page in the top right hand corner, there is a rank.

A, B, etc. If you are good enough at the grand prix, you will get star rankings. (going up to 3 stars) To get at least a one star ranking means that you have to come in first place all four races. (and without ever being in 12th position at any point in the races) To get higher star rankings, just get better times on the courses.