How do you create an alliance?

First, you need to research the Alliance tech.

Then you need a 'close' relationship with an AI race. That is none too easy to obtain. You can't have too much influence over them, your military can't appear weak, you should have established some trade routes with them, and it doesn't hurt to gift them a few techs and money when they are at war with someone.

Once that happens you should see an 'Alliance' option in the trading screen. Offer that to the AI you are close with and choose 'OK'. If they don't accept it on the first try, try adding some incentives (like some money, ships or techs).

Don't you also have to make sure that the AI has the Alliance tech before it will work?

Thanks! 

Obviously I've already blown it in my current game...

Easy enough to give it to them.

Yes, but you didn't mention it in your post.

"should have established some trade routes with them, and it doesn't hurt to gift them a few techs and money when they are at war with someone."

Does it make a difference if the proposed ally partner is at war or not when gifting them something? Do they appreciate it more when they are at war?

Tip: be careful when joining an alliance, because you can easily get into an universe-wide war if your ally is not very cautious or a warmonger or weak military.

After you achieve a "close" relationship with an AI that you want an alliance with, check their technology to see if they have the "alliance" tech.  If they do not have it, as was noted above, you can trade or give it to them.  However, there is one mistake I have made that you can avoid.  Do NOT close out of the communications window with that AI once you have traded or given them the "alliance" tech.  If you do, you will have to wait out the normal interval before you can approach and talk with them again.  Thus, get them the tech and then do the alliance in the same session.

Also, one good thing about an alliance is that the AIs NEVER break them with the human, though the human can break them with the AIs.

In some ways, yes. If a war goes bad for a civ it might take their Military Rating down - so they will more look up to you, which might translate into a strong diplo bonus.

The other thing is that they occasionally ask you to help them. Gift them something (until the dialogue gets green) and you'll get another strong bonus (+ they appreciate our past help).

AFAIK the game will ask you if you will honour the alliance, so you can even step out of this alliance-war right off the start. The alliance will be terminated if you choose to not help, but the relation will be set to "friendly" from which it is easy to have "close" again.

True, though sometimes the alliance doesn't show up either. In this case, gift the AI a few techs until he makes a joke about your " brown nose" etc pp; if he's willing the alliance will pop in right then. Otherwise you need to wait for a few turns.

BTW, there seem to be no possibility to ally during the first 3 years of a game.

I've not experienced that behavior!

That is, once I get the AI the alliance tech in the sequence above, the alliance option has appeared.

I have eased off playing recently (DA).  I have never had the Peacekeepers event or the Pirates one, though I have played a lot of games.  Even the DLs seemed to have stopped showing up in my Suicidal games.

Does Suicidal turn off some of the mega events?

  ...and you can easily have suddenly "signed a peace treaty" if your ally decides to make peace with a common enemy.  Great if you want peace but won't give up half your planets and most of your techs for it;  you get it for free.

  I think this can only happen when you are attacked and your ally decides to help - then the enemy later signs a peace treaty with your ally.

Are you sure this is possible? I seem to remember plenty of occasions where I was attacked and my ally signed a peace treaty with the enemy while I remained at war with them. I could be mistaken though, it's been a while since I had any allies during war time

   Yes,  it happened in a (metaverse, DA) game I was playing a few minutes before I posted my reply.

  That is what usually happens with me too.

I've had my ally apparently make peace for me at times. It's rare, and more commonly they sign a separate peace, but it does happen.

Thank you both... looks like I need to wage more war when I have allies rather than by myself 

For all you said, really? I played a game with the altarians on the ultimate intel, only them, I only had my homeworld and another with the best quality I could find, I traded the allaince tech from them, and than I waited more to bring the neogoitiate screen up, boom, allaince, I won. You don't need any of those things, just the tech.