It’s been a long-held wedding tradition: Save the top tier of your wedding cake, wrap it up, stow it in the freezer, and eat it on your first wedding anniversary. This tradition goes back through the years, growing out of a time when wedding cakes and baby christening cakes were basically the same thing, and couples usually had a baby within a year of their marriage. It made sense to save part of the wedding cake for the latter event. It also helped that these wedding cakes back then were primarily fruitcakes, which did not require refrigeration to prevent spoilage.
Like many “traditions”, saving part of the wedding cake is one that we think is going away. You do not have to do this. A lot of bakers nowadays are providing a free anniversary cake one year later — ask your baker if they will do this. No matter how well you try to preserve the cake, it’s not going to taste as good as it did on your wedding night. Or, just go out for a nice dinner and dessert on your anniversary. It’s up to you!
If you really want to hew to tradition, wrap it really well in plastic wrap and then in an airtight container. You should put it in the freezer that night. And then yes, on your anniversary (or the day before) you would thaw the cake and have it for dessert.
But again — we feel that this is a super optional tradition and most people these days do not do it.