Take off an old toilet seat by uncovering the hinge bolts and backing out the nuts underneath, even when they're corroded.
At the back of the seat, two plastic caps hide the hinge bolts. Slide a flat-head screwdriver or fingernail under the edge of each cap and flip it up. Some hinges have a sliding cover instead — push it back to expose the bolt.
Reach under the bowl rim to find the plastic or metal nut on each bolt. Hold the nut steady with one hand (or a wrench) and turn the bolt counterclockwise from the top with a screwdriver. They usually back out by hand once started.
If a metal bolt is rusted and the whole thing spins, soak it with penetrating oil and wait 10 minutes, then grip the nut with pliers. If it still won't budge, cut through the bolt with a hacksaw blade or a small rotary tool, protecting the porcelain with tape.
With both bolts out, lift the whole seat straight up and away. Wipe the two mounting holes and the porcelain around them with a disinfecting cleaner before fitting a new seat.