Greens fees vary depending on the type of facility and the golf market where you live.
First, golf markets: Some cities have a plethora of public golf courses; others are top-heavy on private courses with just a few public options. The golf market, like everything else in a capitalist ecomony, is driven by supply-and-demand. In cities with fewer public golf courses, or cities in which the golf market caters to resort tourists, the fee will naturally be higher.
In cities with plenty of public golf, the fees be lower. Especially in cities with many municipal (city-owned) golf courses.
Second, the type of facility makes a huge difference in how much they charge. Private country clubs are off the charts, and most of us can't play them anyway.
Resort courses - golf courses that are operated as part of a resort complex - can cost hundreds of dollars to play. They exist for the luxury traveler, not the average golfer (although they are usually open to locals, too).
Daily-fee courses are public courses that are owned by private companies, as opposed to city or county governments. Depending on the construction and maintenance costs involved, the geographic location and many other factors, daily-fee courses can be as cheap as $25 per round (for 18 holes) or as expensive as resort courses (hundreds of dollars).
Municipal courses - those owned by cities or counties - are the cheapest, with some costing as little as $15 to walk. Munis can also be as expensive, however, as midlevel daily fee courses.
Cheapest of all will be the small-town 9-hole course, where a golfer might be able to pay less than $10 (minus a cart) to play all day.
Renting a golf cart will add more dollars to the round at many places; at some, a cart is built into the greens fees.
Some courses require the use of a cart, but most give the golfer the option of walking. Not all that allow walking, however, will discount the greens fee just because you are not taking a cart. (If you are willing to walk to reduce the costs, be sure to ask if it's cheaper for walkers.)
Want to further reduce your costs? Check into executive courses and par-3 courses (which are a good place for beginners to play regardless of budget). They usually cost much less than even municipal courses.
Then, of course, there are driving ranges and practice areas where you can hit a bucket of balls and work on your chipping, pitching and putting, usually for less than $15.
If you want to play on the cheap as you're just starting out, you'll simply need to make some calls to courses in your area and compare rates.
Also keep in mind that at many courses, tipping is expected and will add to your costs. Beginners who play mostly at municipals or 9-hole courses likely won't have to tip.