You can, via a wireless router but you won't be able to access the Internet.
Let me explain,
WiFi does not expressly imply a Internet connection, although it is common.
An Internet connection is provided by a connection to an ISP such as At&t, Comcast, Verizon, Etc.using the proper modem. (DSL, Cable, Etc.)
This Internet connection can be shared with multiple devices ether via WiFi or Ethernet with the addition of a wireless router that connects to the modem.
WiFi has very limited range, a few hundred feet at best. Wireless signals are affected by many factors including distance, wall density, electrical interference, directional antenna range, etc.
That being said,
Internet speeds and pricing vary greatly by geographical area. Various Internet plans are sold with specific speeds (Mbps) and monthly fair usage limits (data caps).
Depending on your exact location, you may be able to choose from several different types of broadband Internet access. They include DSL, cable, fiber, satellite, and wireless from a cellular provider.
DSL is generally the cheapest broadband option, however it is also usually the slowest. DSL Internet is transmitted over standard twisted pair copper telephone lines. DSL speeds typically range from 256 Kbps to 12 Mbps.
Cable Internet is transmitted over coaxial television cables. Cable Internet speeds range from 1 Mbps to over 300 Mbps. The speed of the service depends on your exact area and service package that you order.
Fiber optic services can be as fast as 1000 Mbps https://fiber.google.com/about/ , Fiber connections can also provide on demand HD television and digital telephone service on the same line.
There are also 3G and 4G wireless mobile broadband services and satellite Internet, but these are normally only used where cable or DSL are unavailable due to the higher cost, slower speeds and low monthly bandwidth limits.
If you are in a truly remote area (the woods), you may only be able to use satellite or cellular, both of which are expensive if you want to use a typical amount of monthly data.
To compare speed and prices of your local competitors, go to a ISP comparison site that lets you input your address, and compare the pricing and terms of the offers that are available in your area. In the US you can use this one http://isp1.us/find/ otherwise do a search for "ISP comparison" at your favorite search engine.
The physical address is needed because some services, particularly DSL, are very distance sensitive. For example you might be able to get a specific level of service while your next door neighbor can't.
You'll want to pick the fastest plan that fits your budget. In some areas this can be 300 Mbps+. But these high end broadband plans are expensive. You may find that something in the 10 to 50 Mbps range might satisfy your needs at a much lower cost.
Many ISP's include a wireless router as part of the package, if not wireless routers are fairly inexpensive. http://www.amazon.com/s/?_encoding=UTF8&linkCode=ur2&camp=1789&creative=390957&field-keywords=wireless%20router&url=search-alias%3Daps&sprefix=wireless%20ro%2Caps%2C490&tag=excharge-20 , the brand is not as important as the model. Some manufacturers release a good model but the next is crap. I would look at the Amazon reviews of models that interest you. Even if you don't buy from Amazon the reviews will tell you a lot about which models to avoid. Look for at least 15 or more reviews with a 4 star or better rating. Read a few and see if they sound like the particular model will work for your application.
Good Luck...