As B_B has said, it's easier to tip the mower back, and get the old oil out that way. If you really want to pull a drain plug, the rear one won't make quite as much mess.
Stated oil capacity for these engines is 600mL, but don't be surprised if you can't get quite that much in.
Correct fill level is to the lower edge of the filler opening; i.e. just to the point of overflow, with the mower parked on a level surface.
We recommend the use of a straight SAE30 oil, not a multigrade, in side valve Briggs engines. They always seem to burn a fair bit more oil, with multigrade.