Depending on the dimensions, you may be able to find boards that save you from having to make cuts.
Trash and recycling storage is important. Not all of us like to see garbage cans, either. So, creating a tall storage box with compartments for each can make for a simple woodworking project. Depending on the dimensions, you may be able to find boards that save you from having to make cuts. Just make sure that they are screwed together using wood screws to support the weight.