Well, first you will need to download it, and install it. If you aren't sure how to do that, the Curse Client will do it for you! Once you've done that, head into the game and just type in /oq, or hit the little oQ button you'll notice hovering around your minimap. Like any addon that scans your character, you'll need to "show" it information like your rating (open your PvP window) and your gear (character window) if it's having trouble picking those up.
Once you've got all that set, which should be a matter of moments, hit the "Find Premade" tab, and you should be greeted with a window that resembles the one in the header image. Within that, since the launch of patch 5.3, there have almost always been several LFG requests like you see above. Yes, I play in the EU, and over here HC is an abbreviation for heroic. I believe it stands for hard-core.
This was in the daytime, at about 11am, so hardly high-traffic timing, and I have used oQueue to PuG rated battlegrounds and heroic scenarios at every hour of the day. It works using your battletag, so don't be alarmed by suddenly receiving lots of friend requests, it will delete them again for you too, unless you choose to add them yourself. There is a checkbox at the bottom to only show premades you are qualified for: there are often premades with item level requirements, as you can see above.
As long as you meet the requirements, all you need to do is hit the "wait list" button. If it was successful, it will then change to a "pending" button, as you can see above. Then, just wait! And you can, of course, also create your own premade, using the "Create Premade" tab and inputting the details. It's all very straightforward, and it's not yet taken me longer than five minutes to find a premade for a heroic scenario. Happy pugging!