Proxies are things that use another IP as yours, therefor hiding yours. There are four types of proxies:
Transparent Proxy- The proxy is known as a proxy, and the original IP is shown in HTTP headers. It isn't that great for anonymity, but it will get you around IP bans from sites.
Anonymous Proxy- The proxy is known as a proxy, but the original IP is unavailable. This is an alright source of anonymity.
Distorting Proxy- The proxy is known as a proxy, but it replaces the original IP with a fake or 'distorted' and is shown in HTTP headers.
High Anonymity Proxy- The proxy is not known as a proxy and no IP address is shown.
There are proxies used via internet and proxies used via downloads.
The most common proxies are used over the internet, and what you do is you go to the proxy's website, and browse the internet through the proxy site, therefor displaying the site's IP as yours.
To get proxies, here is a site that has tons of proxies:
http://proxy.org/cgi_proxies.shtml
There are thousands of proxies there.
There are downloadable programs that are proxy switchers. What it does is you upload a list of proxy IPs and it uses them and switches them at predetermined intervals of time.