You need to, in a way "Beat" the game. Race Grand Prix and finish all 32 tracks. If I remember right that will allow you to use your Mii online. Have fun.
It is a lot to think about. If you want to get a high rank online, you will also need to get your rank up in the game. Example, some online players have the Wii Wheel next to their name with a star ranking (1 star, 2 star or 3 star) you will need to get a 3 star average on all tracks at all cc levels offline. So it is really more like 128 races. (50cc, 100cc, 150cc and Mirror Each at 32 races.)
Also; if you have a 3 star rank on 31 tracks and a 1 star rank on one, your rank will show up as a 1 star online.
So you are always equal to your lowest ranking offline when online.
PS as you progress in the game the “Mirror” tracks will open. Same tracks, just a mirrored reflection of them. Yeah it is tough especially after you master the tracks the normal way.