This walkthrough covers exactly where Ableton Live keeps your sound packs and how to get them working in a project. Packs you already own sit under Available Packs in the browser, separate from ones already installed. After buying a pack from the Ableton webshop, right-click Available Packs and hit Refresh to make it show up for download.
Once downloaded, an install icon appears, and clicking it locks up Live until the pack finishes installing. After that, the pack expands into its folders so you can browse what's inside.
Loading presets and clips into Arrangement or Session view just takes a drag and drop, or a double-click if you'd rather skip the dragging. First-time installs also drop extra info about the pack into the Lesson view, worth a quick read before diving in.