You can add floating plans to the fountain, such as waterlilies. They will float on the surface of the water to shield it from egg-laying mosquitoes.
You can also stock the fountain with mosquito fish, guppies, killfish, or another type of fish that eats mosquitoes. They won't stop the mosquitoes from laying eggs in the fountain, but they will kill the larvae.
Here are things you will need if you are making the water feature yourself in a container:
1. Container (pot without holes, galvanized tub, etc.)
2. Pump or air bubbler
3. Floating plants
I'm going the route of galvanized containers and using pumps from Home Depot.