As a staunch EP player, I forgive you for your poor choice of faction and look forward to meeting you on the field of battle!
That being said, do you have a campaign/style in mind?
For PC/NA, you have
No CP, 30-day Sotha Sil - I'm not very familiar with this campaign or how busy it is. You won't get the benefit of damage or mitigation or sustain from your CP, which players who enjoy no CP swear up and down is the most balanced way to play. So if that's your cup of tea, look for groups on Sotha Sil.
CP, 30-day Vivec - Vivec is the busiest campaign, and you'll find some sort of semi-organized PVP going on at all hours of the day or night. It also tends to be the laggiest server, especially during primetime when there are tons of players. I play EP on Vivec and I know that AD has quite a few good groups/guilds running having defeated them and been defeated by them many times.
CP, 7 day Shor - Shor is a much less busy version of Vivec. It has a small population most of the time, but picks up pace during primetime. Shor is where the groups that want CP but don't want to deal with Vivec's lag and tons of players play. Small groups and organized guilds can make a big impact on this campaign.
No CP, below level 50 Kyne - Kyne is only for below level players, so its a great way to learn PVP with a bunch of other people of varying skill levels. Or its a great place for experienced PVPers to take low-level alts out in gold gear and wreck face.
All of those campaigns will have different groups and organized guilds running on them.
In any campaign, there are the old standbys of typing "LFG" in zone chat, and you'll quickly get a feel for which groups are actively picking up members in your faction. I found my PVP guild by following the organized raids around until I finally gathered up the courage to get in TS with them, and then joined the guild after realizing I liked running with them.
So good luck finding an AD group that will welcome you and your talents, and if you play on Vivec, maybe we'll see each other in death recaps someday!