What is the most common method to find a group for a Flashpoint?

Solution 1:

In my experience, being in the fleet and going "/1 [my class] LFG [name of flashpoint]" works reasonably well.

Alternately, paying attention to General and responding when someone goes "[flashpoint] group LF[number]M" for much the same reason.

EDIT: Update 1.3 introduced the Group Finder Queue, and gives out bonus commendations once a day for using it. Learn it. Use it. The more people who use it well, the better it works.

Solution 2:

Gather in the flashpoint location and flag yourself in /who or in the Social window (Press "O") as LFG, you can also leave a short note there (E.g., "LFG Hammer" or just "hammer"). You can then search for people with LFG tags. It's nice tool, but it's a shame not many people use it.

Solution 3:

With the recent addition of patch 1.3, the Group Finder is by far the easiest/most effective way to get groups together for flashpoints (both heroic and normal), story-mode Operations, and heroic quests on planets.

It's available from level 10 onwards as a tab next to the minimap. See the linked official guide for full details.