phpMyAdmin requires MySQL (duh) and the mycrypt PHP extension.  You can follow the link below for Windows (up to Vista) but the key things to look for are:

1. Copy ‘libmysql.dll’ to the ‘bin’ directory of the Apache installation.
2. Copy ‘libmcrypt.dll’ to the ‘bin’ directory of the Apache installation.

Both of these files should be in the PHP installation directory.

Additional Notes

DO NOT under ANY CIRCUMSTANCE copy DLLs to the Windows system directories.  It is not advised, recommended nor permitted under good software practices.

Additional Links

Configuring PHP with MySQL for Apache 2 or IIS in Windows

EDIT:

OK, so I got phpMyAdmin up and running and noticed because I chose the UTF-8 (multilingual) install I needed the ‘mbstring’ extension installed.

Another note of possible concern (but can be safely ignored) is a message similar to:

Your PHP MySQL library version 5.0.51a differs from your MySQL server version 5.1.31.

You can actually solve this problem by using the ‘libMySQL.dll’ from the MySQL ‘bin’ directory.