So you were lucky enough to inherit a memory foam mattress topper, but it's too big for your bed. Don't fruitlessly try to tape down the sides, cut that foam! Cutting memory foam is not nearly as hard as you would expect.
Though it is possible, cutting your memory foam mattress topper with a pair of ordinary kitchen shears will be difficult, time consuming, and will leave you with painful red marks where the scissors continually rapped upon your hand. Instead, use an electric knife! Most people have electric knives around the house for cutting the Thanksgiving turkey or Christmas ham. If you don't have one, ask your neighbors.
The next step is to measure your bed. Subtract 1/4 inch from the measurement of each side, and then draw those dimensions directly on the foam with a thick pen or marker. You want to cut the foam a tiny bit smaller than your mattress so that you'll have no problems pulling your sheets over the mattress topper.
Pull the foam on top of a table, with the end you plan to cut first just over the edge. Then use the knife as you would with a turkey, pushing lightly on the knife to cut a clean line through the memory foam. Be careful; as you wouldn't pull up and down with the electric knife on your family supper, you should use care when cutting the foam as well. The vibrations of the knife will force it to cut a straight line, but if you push and pull too much, too fast or too hard, you will get jagged edges on your mattress topper.
Once you've successfully cut the first side, repeat this on the other three sides and soon enough you'll have a new memory foam mattress topper sized perfectly for your bed!