Evidently some people are having problems figuring out how to use a proxy to hide his/her IP, mainly random users on my MSN and AIM lists, though I've seen several threads asking for help here on GamingGutter as well. This will cover only the newest versions of FireFox and Internet Explorer, though the methods may be different for other browsers, it's all essentially the same. This guide isn't meant to educate what a proxy is, how it works, or what it does, but how to get what looks like random numbers to actually do somethings.
Regardless of your browser, the first thing you want to do is find yourself a proxy. I normally use AliveProxy, and down at the bottom of the site you'll see a whole bunch of selection, I stick to either
Fasters or
8080 port proxies, depending on my needs. At home I go with Fastest because they're the most efficient, but at school I used to get 8080 because that port wasn't blocked by the school, which allowed me to bypass Websense, which is the school's site filter.
When you get something that looks like "85.217.183.27:3128" you know that every number before the colon is the IP, and every number is the port, and the colon is simply used to separate the two.
FireFox:
1) Simply to go Tools>Options>Advanced>Network>Settings>Manual proxy configuration.

What you're doing now is establishing a connection through the IP of the proxy, so when you're on a site, that's what it'll show, instead of your own on.

2) Now in the HTTP Proxy bar, type in the IP, which in the case above would be 85.217.183.27
3) In the Port bar enter the port, which is 3128
4) Hit Ok on both windows
5) You should be set with your "new IP," though isn't yours, it'll appear to be. You can confirm that it shows something different by going to sites like
this.
Internet Explorer:
1) Go to Tools>Internet Options>Connections>Setup

2) Check the button that says "Use a proxy server for your LAN"

3) In the Address bar type in the IP of the proxy, which in the above case is 85.217.183.27
4) In the Port bar enter the port, which is 3128 in the example above
4) Hit Ok on both windows
5) You should be set with your "new IP," though isn't yours, it'll appear to be. You can confirm that it shows something different by going to sites like
this.
Now sometimes the proxies will be slow, or won't work at all, so I suggest using a program to at least check if the proxies are still alive. Charon is a rather familiar program, but I use
this because it's a small file, quick, and simple to figure out.
Using PPrx_Chk
1) Go to the Options tab, and under Connect to type in a website, or use one from the drop down box.
2) Go to the Main tab and find the source file (that's the one that has all of the proxies listed. They should be displayed IP:Port and one per line, like so:
12.43.216.56:80
85.45.34.1.3:8080
Those numbers I got by just hitting the keyboard randomly, so those two won't work)
3) Pick a file where you want the good proxies to be saved, and then hit Run
4) Wait for it to finish, then open the file that you specified the good proxies to go. The ones that are not in that file won't work, so they aren't saved.