There are 7 main ways to redirect or cloak your links:

Simple PHP Redirect

Short and sweet, requires just one line of PHP code in a file that's then uploaded to your web site. Even a non-programmer can easily learn the one line of code that's needed. The downside is that each link you want to cloak requires a new file to be created and uploaded. Also, there's no easy way to track the clicks on the links.

HTML (META) Redirect

Eay to use, just needs one special line of HTML code in the title section of a web page. Like the PHP redirect, it requires one file per link, and there's no easy way to track the clicks. Also, there is some suggestion that Google doesn't "like" links that use the META Refresh tag -- do some research before relying on this method.

Javascript Redirect

Quick and easy, but again, it requires a new file for each link and has no good way to implement tracking. Also requires that the use has Javascript turned on in their browser.

HTACCESS

Probably the most "geeky" method of redirecting a link, it requires you to modify the .htaccess file on your web site. Since making a mistake in that file can take down your entire site, it's not a method I recommend. Again, so good way to track clicks.

Framed Redirect

This is the "fantasy" cloak since it also hides the URL in the browser. Unfortunately, it can't be used for a lot of affiliate programs (such as Clickbank) as it's against their Terms of Service. It's also been my experience that it's unreliable so it's not recommended for promoting products with an affiliate link.

Hosted Solution

TinyURL is probably the most used hosted redirect service right now. It's incredibly fast and easy to create a redirect URL. However, the downside is SO far down that I don't ever recommend using a service like that. In a nutshell, you have no way to modify the redirect once you've set it up. Which means you could be sending traffic to a dead site, a site that's stopped their affiliate program, etc.

Self-Hosted Solution

This is almost a hybrid of the PHP redirect and a hosted solution. You get the ease of a hosted solution with the ability to change the redirects if you want. A good cloaking solution will also do tracking at the same time -- make sure the one you choose does both. The downside is that you'll probably spend about $50 (one time) to get the software -- consider it an investment in building a more profitable business.

Those are the most commonly used methods of cloaking a link, either to hide an affiliate ID or to make a long link much shorter. There are free solutions and paid solutions -- choose the one that's best for your business (and that's able to grow along with you as your business grows).