To get Archeage (optionally Rift & Defiance, and possibly Trove), is to go here: Glyph - Account Management
Install the Glyph client (The games will be installed to the Glyph folder by default, so choose well). If you have a Rift, Defiance, or other Trion Worlds account, you can use this to sign in to Glyph - otherwise register a new account.
Select the game you want to install, press the button, and wait. 
Archeage works out to around 23gb right now (installed and uncompressed). If I remember correctly, the initial download was around 15.8Gb, but has probably increased slightly with the last several patches.