First, what is tethering? Tethering is the ability to take the 3G/4G internet on your phone and use it on your PC. So if you are somewhere where there is no wifi but would like to connect to the internet on your laptop, just use your phones internet on your computer.
Just yesterday it was announced that the FCC has told verizon that it can no longer block apps from the Google Play store that allow people to tether their phones to the computer. Why was verizon blocking them? Because Verizon offered its own service that did this which of course was $20-$30 a month (I cannot recall actual price but it was around there). So now you can download those apps and use them for free. Yay!
Now notice I did not mention apple but only google. Apple has complete control of their app store and blocks these app, so iPhone users are out of luck for now. The only way to do this with your iPhone is to jailbreak it.
So what are these apps I speak of? The most popular is probably PdaNet. This app offers both a free and paid version. The free version will allow you to connect to any website for free unless it is an HTTPS site, meaning you cannot connect to your email. If you pay $15 you will be able to connect. So feel free to download and use. You no longer have to worry about getting in trouble, however, please watch your data usage if you do not have the unlimited plan.