Proxies are not hard. I've found most guides to be rather dense and complex; so here's a quick one.
First of all, you will need firefox. It is the only browser that I know of that supports proxies EASILY. Yes, technically you can create proxies in Chrome or IE but it's hard. Firefox is also the best option for using grease monkey scripts. In short, you need Firefox if you are doing anything illigit on neopets.
Now, for proxy info: A proxy makes it look like your computer is accessing whatever from somewhere else. This means you can make accessing 10 different accounts on your computer look like access from different parts of the world. Because the interwebz has to go through whatever to make the connection, proxies are often painfully SLOW. Luckily, neopets only records your IP on LOGIN AND LOGOUT
EDIT: It is suspected that IP's are also recorded on PASSWORD AND EMAIL CHANGES
Here's a little tutorial on using (you need an account to see links) with firefox.
Here's what your page will look like:
You want ones that are HTTPS and HIGH+KA because these hide your identities the best. I don't know about socks4/5 but they should work fine too; I just never looked into them.
Now, here's a little diagram of the parts:
Speed is not at all important, but connection time is. Make sure the connection time is at least green, and try to get a speed of at least mid-red.
Here's a little diagram of the steps to enter your IP and PORT
And now you are using a proxy!
For TOR: Download it (you need an account to see links)
And then open the browser and go to the same place as the firefox one:
That button for new identity will be on your onion control panel thing, you press this to use a new identity.
You can just use the tor browser but it is very slow and blocks all plugins.
So, copy and paste the numbers and set up everything to match what you see on the tor browser to firefox.
Now, when you press the button you will use a new identity on firefox and can switch back to no proxy whenever you want!
Tor assigns you a random identity from it's list, essentially doing what you would do with manually choosing a proxy and entering it yourself. On the downside, there are a finite number of these proxies so if you login to an account there is a chance that another person has logged into an account on the same network; as far as I know this has not created any problems though.