How do you get rid of radioactive waste?

Radioactive waste disposal involves finding a safe place to store it until it’s no longer radioactive. Different types of waste give different levels of radiation. Radioactive waste disposal is divided into three general categories: low level, intermediate level, and high-level waste. Low-level waste typically has short-lived radioactivity. It does not require cooling nor shielding to handle. An example of this would be a lab coat that has been contaminated by radioactive material. It is disposed of through shallow land burial.
Intermediate-level waste requires shielding to handle but not cooling. An example of this would be metal fuel cladding at a nuclear power plant. This type of waste is stored at a nuclear waste repository. Please note that the United States does not define this category, but other countries do. High-level waste requires both shielding and cooling to handle.  Used nuclear fuel is an example of this. High-level waste is stored in a deep geological repository.
There are other waste categories, but this should be enough to get you started. See the links below for further research.
https://www.world-nuclear.org/information-library/nuclear-fuel-cycle/nuclear-wastes/radioactive-waste-management.aspx