You can find dungeons pretty much anywhere, they are the little torch icon. But some of them are group only, meaning you only enter with the group you made. The majority of them are public dungeons, so you'll see random people in there with you and can get help from them if you need it. The group dungeons have a plus next to the torch.
As far as the LFD, I see people posting in Zone chat all the time looking for groups, that's the only way I'm aware of. And, someone correct me if I'm wrong, all the group dungeons, are only 4 man groups. The one time I went in with a group of 5 it glitched really hard and one person was always invisible, which makes me believe you're only suppose to do dungeons with 4 people.
Yes, the torch+ dungeons are instanced and for groups of 4 (or less if you're just that OP), there is a LFD option, if you press P to open your group window, at the top right there is a magnifying glass, clicking that brings up the group finding function. It doesn't really tell you when you found a group though, you just get put in it, sometimes so fast that by the time you close the window out you are already in a group.
If you use the group tool, you can select a dungeon or zone that you want to find people for. You can queue as a tank, healer and dps. It would help the group a lot if you pick a role that reflects your character.
While I didn't try the "zone" search yet, finding players can take a while especially as a DPS. My tank last time had instantly a group
I do believe group dungeons are denoted by a torch+ symbol and they mean group. Mobs come in at area level in groups of 6-10 (counting adds), with the boss being brutal.
Largest group I was in was 6. After 4 people you get classified as being in a "very large group."