There are many methods but meta refresh is NOT the best one!
How good are you with php?
I wrote a simple script that grabs a variable from the url string, matches the variable to a pre-defined affiliate url in the database and redirects to the affiliate page.
Basically, all my affiliate urls are like this:
example.com/myscript.php?id=376
I also make sure all these links are "nofollowed"
When somebody clicks this affiliate url, the script will check the database and find which partner is id 376, retrieve the url and do this:
header("refresh:1;$url");
I also place a Google conversion label on myscript.php because I occasionally use PPC and it helps me track conversions. You can place your current tracking code there too.
You can also track the referrer (i.e. your internal page url that generated the click) and the visitor's IP address, and some other metrics, depending on how much detail you need.
I've found that it's beneficial to have full control over the affiliate links.