Payment Form is a Joomla extension, so you need to have a website built on Joomla CMS to use the extension. Please look at https://www.joomla.org/about-joomla/technical-requirements.html to see technial requirement for your server. Payment Form only works with Joomla 3.x, it doesn't work with older versions of Joomla (Joomla 1.5, Joomla 2.5).
Beside generic requirement with a Joomla website, Payment Form also requires one additional requirement. If you use a credit card based payment plugin (for example, Paypal Pro, Authorize.net, Eway, NAB Transact...), customers will enter credit card information directly on your site for processing payment, so your site should have an SSL certificate installed so that the payment process will be secure. Without an SSL certificate, Payment Form still works well, however, in this case, the credit card data which customers enter on your site for processing payment won't be encrypted when it is transfered over internet, and it will be inscure.