ESO Alliances Guide
The first decision a player has to make when getting started playing The Elder Scrolls Online is which alliance that they want to play. In TESO, there are three alliances that you can choose from: The Daggerfall Covenant, The Ebonheart Pact, and The Aldmeri Dominion.
Each of the alliances has a rich history and tonnes of lore, especially regarding how each alliance was formed, why there is so much tension between the alliances (see the PVP guide for more information on the Alliance War), and more.
However, I think it's safe to assume that you're here because you want to know what it's like to play in each alliance moreso than for the history and lore of each alliance. (If you do want information on the history and lore of the alliances, though, here's a link).
Choosing an Alliance
I suggest that choosing an alliance is almost more important than choosing your race. I say this because your gameplay experience, especially early in the game, varies greatly between each alliance's zone.
Given that you can customize any character/race to play how you want, it seems to me that playing in the environment and zone that suits you the most is probably the most important choice you'll make early in your TESO adventure.
So, with that said, here's my view on how each alliance and zone feels to play.
The Ebonheart Pact
The three races that make up the Ebonheart Pact are the Nords, Dark Elves, and Argonians, and none of them really like one-another. That alone should give you an idea as to how this alliance feels to play, but allow me to clarify.
The Nords are conquerers, the Argonians are guerrila fighters, and the Dark Elves are, well, Dark Elves.
Overall, the feeling you get when playing in the zone is one of tension. The Pact is barely holding together, and with the scheme of Molag Bal now in play, the Pact is being stressed even further.
Combine that with the cold northern climate that makes up the environment of the starting area and we have the makings for some pretty deep characters.
Interacting with non-questline NPCs in the zone definitely gives the sense that Tamriel is under threat, with many characters having a miltiary personality--all business.
Of the three alliances, The Ebonheart Pact feels the most serious to play... serious as in serious characters, not as in more hardcore players.
The Daggerfall Covenant
Bretons, Redguard, and Orcs compose the Daggerfall Covenant, and this alliance is the opposite of The Ebonheart Pact. By that I mean that the three races are unified under a great leader, and each wishes to be in the alliance. This causes the overall feeling to be less serious than in The Ebonheart Pact, but not as light-hearted as The Aldmeri Dominion.
Genrally, playing in this zone feels more "human" to me. By that I mean that there is more everyday stuff going on... a guy admiring a statue, and couple in love, a pesky dog, and so-on.
The environment in this zone is warmer than that of The Ebonheart Pact, but not tropical.
Interacting with non-questline NPCs is generally more personable, but that's not always the case. Guards are still quite brusk, and not everyone is friendly.
I'd say that The Daggerfall Covenant is a good combination of serious and light-hearted gameplay.
The Aldmeri Dominion
The Aldmeri Dominion is made up of High Elves, Wood Elves, and the Khajiit. This alliance was formed because each of the races has aided one-another, and they now stand strong as one.
The feeling I get out of this alliance is the most light-hearted of the three alliances. The Wood Elves and Khajiit are funny by nature, which is a good offset to the more serious nature of the High Elves.
That's not to say that there is not serious gameplay to be found here--in fact I found probably the most serious early questline in this alliance's zone--but overall, playing in this zone feels a little lighter.
Speaking of a lighter feeling, the tropical climate and palm trees definitely play their part in that.
As for interaction with non-questline characters, I would say that the NPCs in this alliance are generally the most entertaining of the three alliances, but as with all of my comments for each of the alliances, this is the overall feeling I get and is not always the case.
The Aldmeri Dominion feels like the most light-hearted alliance to me, with its entertaining dialogs and pleasant climate playing a large part in that.