Seat is Loose
Toilet Seat bolts are loose or damaged
If the bolts are loose, use a flat head screw driver to hold the bolt steady and gently tighten the nut underneath the seat with adjustable pliers. If the bolts are corroded or damaged they will need to be replace. Be certain to purchase the same size bolt from the hardware store. To loosen corroded bolts you may need to apply penetrating oil and let it set for several hours. If that does not work you can use a hack saw to remove the bolts.
Toilet Seat is cracked
If the toilet seat is damaged and needs to be replace remove the bolts in the manner described above and lift the seat from the bowl. Be certain the seat you purchase is the same width and length as the one you are replacing.