There are some modest costs for this service, but depending on your situation you may be able to get around them too. The monthly fee is $4.99, which would almost certainly be worth it for frequent travelers or people who live outside of the country and have Fires. But there is a 7-day free trial that could probably cover you for your next trip. You'll be able to give it a try and essentially use it for free the next time you hop on a plane to go somewhere.
Here's a little bit about how to set up the service while on the Fire (ignore text on this graphic). You're going to want to go into your advanced WiFi settings and go to the following page for setting up a Static IP address. Turn Use static IP on, and then follow the directions on their Android Setup Page. You'll want to copy over the IP address, then "Set Gateway as router IP (usually the same as current IP except last number is .1, i.e. if your phone IP 192.168.2.130 then router's likely 192.168.2.1)," then "Set Netmask 255.255.255.0," and set DNS 1 to 22.214.171.124 and DNS 2 to 126.96.36.199, save, and then restart. Obviously if you're not using this service, there's no need to monkey around with the IP settings.
Getting this right may take a little bit of tech-savvy, but there is a great Support Page, where they can help steer you in the right direction. Once you've got the numbers in the right boxes and maybe also you're using their web addresses, you should be able to get access to anything you could back home! Because I don't know about you, but it only takes about a day before I start going through Hulu withdrawals. Note: I haven't personally used this yet, so if I'm missing any important details or you want to let us know how UnblockUS works for you, let us know!