how do you quickly establish cultural influence?

One thing is to make sure your moral is high...

Also, build culture influence improvement...such as propaganda centre etc etc.

Building Entertainment Networks to keep people happy and News networks to increase cultural resistance would be a start. It could be you are being destabilized by someone. That might show up if you use espionage, but I'm not sure.

You can pump money directly into planets for an emergency, but that is no long-term solution.

What is morale like? Don't forget there is a button at the top of the screen that tells you the relative influence of each race in the sector. I didn't notice this until someone else pointed it out to me (top right of main screen). Perhaps by keeping an eye on that you can figure out what is happening.

I haven't run into this problem yet, but I'm just now playing on normal.

Quickly? Get as many good planets in as many sectors as possible. Also, make sure the morale is high (as a previous poster pointed out). Population also makes a difference, so I often go for the population/influence trade goods as soon as I can get them. Also, go for any social projects that aid influence. But I can't stress the initial colonization enough...once I got that down, it changed the entire paradigm for me! Hope that helped!

~SDC~

Yes, the initial rush is vital to influence as well. All your star systems generate influence points that are added up into a giant pool. Then this pool is redistributed across the map based on several factors, such as how many systems you own in a sector and how far away is your nearest star system from a sector. Wonders that increase influence are invaluable for raising this whole overall pool. So are influence resources. Culture star bases just amplify the influence already there.

The quickest way to get a good influence is, therefore, starting with it by having a good position. After that, if any border sectors start weakening, use news networks and morale boosters. Then get those wonders that increase influence built! But, the honest answer is that there is no quick way. Culture victories are best attained by slow, increasingly crushing pressure.

There is also another way to stop a culture bomb in progress: invade a planet or two of the alien that is causing the problem. This drops their overall influence and gives you an advantage. In most of my culture victory games, I have engaged in limited warfare to take out a planet or two along with some bases so that I would gain the edge in both territory and influence.

Best way to increase your influence early on is to stay neutral,on good terms with all majors and start wars between them. No alignment troubles and civs at war have significant drop in influence. Limited warfare can help but rather unnecessary. Good diplomacy is much better. Anyway, that's long-term strategy

I couldn't agree more. You can further the process by researching technologies heavily and then selling the technology to the other races (including minors). Lately, I attempt to take a much for as many months as possible for as many technologies as I can. This ends up giving me a huge monetary bonus (put toward social improvements and starbases) and ends up bankrupting the other races. If you can maintain a strong enough military presence, you won't be attacked and the other races will fight among themselves...but as the quote says...stay neutral or enemies you will have!! LOL

Gerakken, I find there are certain points in the game where my civ simply explodes culturally. Most notable is when cultural exchange centers become available. In my last game, I cranked up the social production to build one on every planet and in a short span the influence structure of the entire map (medium size) was realigned. It would be fun to try a cultural victory on a huge map. I've only played medium, but I could see where different techniques would be required. I've been working on upping the AI competition instead, though.

#1 BB Bling,

In addition to the above, build a SB with culture-improvement modules in Sol's sector. This will secure your cultural borders & prevent defections, or permit former colonies to "re-secede" back into your Empire.

~SDC~

Yes, that is true. It just takes time to build up that pressure. There is a time when a magic combination of population, technology, and social projects all come together. Once that critical point is reached, it is hard to stop you culturally unless a strong rival builds influence wonders, takes more planets, and/or really climbs the tech tree. Especially lovely is the point on the tech tree where artificial planets and planetary destruction (and one other in that neighborhood that I can't remember) give +10% influence each. That is the point I sit back and say to my alien opponents, "You're doomed. Just a matter of cranking the vise tighter."

Artificial Satellites maybe? I haven't actually gotten that far up the tree. I got to Terraforming in my last game, but only because I had a cultural victory wrapped up so far before 2191 (minimum time for the condition) that I pumped up tech instead.

All these are valid and something I also need to implement better. My last two games (normal) by the time I rushed trade goods, traded or developed techs to keep the Drengin off my back (they declared war), I was almost "overcome" by other colors. Taking the Dregs out gave me more of the galaxy and breathing room. Culturally enhanced star bases helped more than anything as it was too early in the game (at least for me) for some of the more advanced cultural things.

I like the war suggestion to gain breathing room!

Ultimately, I could of won culturally but felt that the majors needed more retribution then just being overcome! Like defensively and culturally enhanced Terror Stars ...

I definitely am sympathize with you BB.

The great thing about this game is learning to tighten up one area after developing some sort of mastery in another.
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If you guys are playing on tiny or small maps, you might try medium so you have a bit more breathing room.