Below is a summary. For details see: System_requirements
Web Server: Apache 2.2 and newer
PHP: 5.2.3 and newer.
Database: MySQL 5 and newer
Browser: Flash is required for the simple file upload function (Add > Add Photos).
PHP Memory Limit: 32M should be the minimum for PHP's memory limit if you're restricted to using GD as your image toolkit. Processing images with GD eats into PHP's allotted memory and can get consumed rather quickly with even smaller images.