To complete the group dungeons that don't belong to your own faction, you'll first have to talk to the Undaunted and become one of them (this is optional, if you've got someone else "opening" the dungeons for you).
Talking to them will reveal the dungeon locations (read: map pins) for your current zone/tier.
Complete the group dungeon belonging to your current zone (i.e. your own faction) first. For example, if you start in the Daggerfall Covenant, the first group dungeon to be completed would be Spindleclutch. Once completed, the other two group dungeons of that tier will be open to you.
Once visible on your map and unlocked, you can just click the group dungeon icon to travel there (it's essentially a wayshrine).
Note that each and every faction got their own instances of those dungeons, i.e. you can't group with someone from another alliance to run these dungeons. The story and content are identical though.