The easiest thing might just be to partner with a nearby business and piggyback off their connection.
... but that's no fun to talk about :)
As for as I know, to get "portable" Internet, you have to use a cellular modem. It may or may not be fast enough for your classes. They run at around 500KB / second, so it could work for smaller classes.
To set it all up:
You could plug a cellular modem into one of your computers and share the internet connection.
OR
Verizon just came out with MiFi, a combined cellular modem/wi-fi router, for around $40 - $60 a month. To find out specifics, go to the Verizon Wireless website and search for MiFi (it'll ask you for your zip code and show your local price/availability)
David Pogue explains it pretty well in his article about the new MiFi router, Wi-Fi to Go, No Cafe Needed:
"[In the past,] if you want to get online while you’re on the move, in fact, you’ve had only one option: buy one of those $60-a-month cellular modems from Verizon, Sprint, T-Mobile or AT&T. The speed isn’t exactly cable-modem speed, but it’s close enough. You can get a card-slot version, which has a nasty little antenna protuberance, or a U.S.B.-stick version, which cries out to be snapped off by a passing flight attendant’s beverage cart."
...
"...the MiFi converts that cellular Internet signal into an umbrella of Wi-Fi coverage that up to five people can share. (The speed suffers if all five are doing heavy downloads at once, but that’s a rarity.)"