The quickest way is from a game's page: open "Your options" and choose "Add this game to my collection", as a physical or a digital copy. The same place lets you remove it.
Your whole collection lives on the "Games" tab of your blog. There you can add games with the quick search, mark whether you have the box and inserts, or a digital copy, and filter by system, genre or format. For a lot of games at once, open the system-by-system editor from that page.
Missing a game? You can add it while writing a review, or ask site staff to add it.