For me it automatically wants to download the installer if it doesn't for you then you an try using the Direct Download or Torrent Download buttons. If you don't know what a Torrent is just stick with direct.
Direct Download will download the installer directly from STO. And the torrent will give you a torrent file that will allow you to download STO via a torrent client.
After the file is downloaded... Run the program and install STO.
After STO is installed you can register an account ( if you haven't already) and start playing.
-- Foundry --
The Foundry is a tool that will allow you to create your own missions and share with other players. This is the Foundry section of the forum so this section is here to do with questions regarding the foundry. If you want to know how to get started and use the foundry. Assuming you are not a subscriber. Then will need to earn dilithium 10K is recommended and that can buy you 4 mission slots.
Once a character has 10K dilithium log out and log back in. At the character creation screen there is a small button to the top and right of the screen. It says "Create Content". Click that and it is in this screen that you can buy slots and create a foundry character. Both of which you will need to do before starting creating a mission.
Head over to StarbaseUGC there are alot of tutorials there.