Cats don't have much of a natural thirst drive and instead have evolved to get much of the moisture that they need instead from their prey. I focus my efforts on making sure that the cat's entire diet has enough moisture rather than just worrying about plain water intake.
So, first, make every effort to feed wet food instead of dry food. According to Lisa A. Pierson, DVM:
A cat's normal prey is ~70% water. Canned food is ~78% water. Dry
food is ~5-10% water. Cats have a low thirst drive and they do not
make up the deficit at the water bowl. They are designed to get water
with their food.
Cats on canned food have been shown to consume at least double the
amount of total water when compared to dry food-fed cats when all
sources of water (food and water bowl) are considered.
There's also a supporting study - Effect of dietary water intake on urinary output, specific gravity and relative supersaturation for calcium oxalate and struvite in the cat. Catherine M. F. Buckley, Amanda Hawthorne, Alison Colyer and Abigail E. Stevenson. British Journal of Nutrition / Volume 106 / Supplement S1 / October 2011, pp S128-S130
Other environment enrichment activities (such as the addition of water fountains) can be considered after changing the cat's diet. From observation I've noticed that my cats have very different preferences for what type of water they like to drink. Some of my cats like falling water, some like water that is rising up (from a pump), while others like to drink from a flat surface of water. Since I have a multi-cat home I have fountains that provide all of these different types of water environments.
Cats definitely prefer clean water, so cleaning the water bowls/fountains regularly must be part of the household routine. I choose fountains made of ceramic or stainless steel since plastic can harbor bacteria. I also make sure that they are dishwasher safe so they can be sanitized easily.