There are two ways to access the group finder.
1) Open you Social window (O), click the Who tab and then click the LFG icon near the bottom of the list (looks like a littl group of people, iirc).
2) Click the group finder ison at the top left of your minimap.
Either way, you can then select which Operations and/or Flashpoints you want to do, and whether you want to let the group finder match you with "in progress" groups. Note that it will not help you with getting groups for class missions, planetary missions, or heroics. It only does Operations and Flashpoints.
As for the companion information, open your Mission Log (L), click the Codex tab, and then Persons of Note, and then go down the list till you find the entry for your companion.
This is correct, but also note that the majority of people will still look for groups for Operations in general chat on the fleet. It is just a lot faster, it seems. I've tried queuing up in groupfinder for Operations, but I've never gotten a pop.