The way I usually tackle this is to scribe it to the floor. This assuming it is a cabinet type vanity with a toe kick and not furniture feet.
Anyway..shim under the cabinet until it is touching the wall and level from side to side...you can check front to back, but it is not always possible to have all three conditions at the same time (level side to side, level front to back, and touching the wall.)
Now you will probably have just one corner of the vanity touching the floor and the rest shimmed up in the air. Measure the point of the widest gap between the vanity and floor. Lets pretend it is a half inch. Go and cut (or find) yourself a little block of wood a half inch thick, and also get a pencil.
Set the block on the floor and set your pencil on top of the block so as to trace a line around the very base of the cabinet a half inch off the floor all the way around the front and both sides...(you wont be able to do the back because it is against the wall, dont worry about it.) Now you will have to take the vanity outside and cut off everything below the line. Be careful, this takes a little skill with the skill saw...(hence the name..lol)
Now your vanity will sit flat on the floor and rest against the wall and be level side to side, all at the same time....Professional installation.