Hi bower4311. Welcome to the forums.
There are lots of options for selling online, ranging from simple to complex. The easiest is to use something like PayPal, where you just place buttons on your page and the rest is handled by PayPal.
All the same, PayPal is pretty ugly on its own. You can use other external carts that cost a bit more but provide a nicer experience. An example is FoxyCart, where you can style the payment pages to look exactly like your site, even though they are off-site. Another popular one is Mal's eCommerce (which you can use for free).
Then there are options where the whole site is hosted by a cart provider. These are nice in that you don't have to worry about all the functionality. You just place your products and pay a monthly fee. Examples include Shopify and Goodsie and BigCommerce. There are some smaller ones, too, if you don't have many products, like BigCartel.
Then you can just download the software for an entire CMS and host it on your own server. That gives you a lot of control, but puts a lot of responsibility in your hands—dealing with security, design, coding etc. Examples include Magento, osCommerce and ZenCart.
So there are lots of options there. If you want to keep your site but just add products to it with payment buttons, I'd suggest looking at something like FoxyCart.
Hope that helps.