Check if the pool liner is safe for fish. The more expensive pool liners are likely to have been treated with algaecide, which is harmful to fish (see Reference 1). The liner may need to be replaced or covered; a cheap liner should be the safest choice.
If the pool is filled, completely drain the water. If desired, wipe down the liner to remove any grime or debris, then fill the pool with water using a garden hose or any other source of water.
Add chlorine remover or water conditioner, available at most pet stores, to the water, since tap water has probably been treated with chlorine and contains heavy metals (see Reference 2).
Use a test kit to monitor chemical levels in the water on a regular basis. If any level is off, many products on the market can be added to the water to adjust and correct the levels.
Install a pond filter to the pool. Since pool liners may become damaged by substrate, the only surface in the pool for beneficial bacteria to grow will be the filter medium. Healthy bacteria are necessary to purify toxins from the water, so a very good filter system must be installed for fish to live. If necessary, bacteria can be purchased commercially.
Run the filter and continue monitoring and correcting the chemical levels. Add some goldfish or inexpensive koi to test the waters. If the fish live, it's safe to begin adding fish.