How do i frame a bathroom vanity mirror?

Depends on the type of material you want to use. If it's timber for instance you would make a timber frame - square or rectangle to fit the mirror. Then buy a thin piece of sheet timber and cut to the size of the frame, or just under the size. Lay the mirror down on the floor inside the frame. Buy a really strong glue, put the glue on the back of the mirror and the timber frame. Lay the sheet down onto the back of the mirror and the frame where you have glued. Put something heavy on top of the mirror until the glue has dried. If the timber is thicker than the mirror then you put the sheet down first and put the glue directly onto the sheet. Then you put the frame down on top of the sheet and the mirror inside the frame. Again put something heavy on top. You can also nail the sheet onto the timber if you want extra strength. Once the glue is dry that's it. The mirror will be finished.

You can use a traditional profile molding cut to fit mirror without removing mirror from the wall. Either mitre corners or straight cut and add plinth blocks to the corners Or frame like a window by simulating a header and sill. Check your existing moldings and decide then visit pinterest for examples. I would cut, then paint before putting up so only minor touch up will be needed after. Here is a link to get you started. Hope this helps

Magic eraser and comet

here's a video that might help...