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[theory]

Yeah...that's a common initial reaction to RFTG. 

I like to think of it like this:

Every round, there are five possible things that could happen: Explore/Develop/Settle/Consume/Produce.  The phases don't all happen each round, only the ones that you and your opponents choose.  But the ones that you choose happen for everyone.  For example, in a 4p, if I choose Explore, P2 chooses Produce, P3 chooses Settle, P4 chooses Explore, then this round we will all Explore, then all Settle, then all Produce.

You're going to build things that will give you bonuses during some phases.  Merchant Guild gives you 2 cards every Produce phase, regardless of who chose it.  In the end, you can get a good score either because you build lots of expensive things (helped along with bonuses during Develop or Settle phases), or because you build lots of worlds, Produce goods on them, and Consume them for points (aided with bonuses during Produce or Consume phases).

When you choose a Phase, you get a bonus for choosing it.  For Explore and Consume you have a choice of one of two bonuses (+1/+1 vs +5, Trade vs x2); for Dev it's a 1-card discount; for Settle it's a card after settle; for Produce it's the ability to produce on a windfall.

How the Explore/Dev/Settle phases work are pretty straightforward.  Get cards.  Pick cards to build, then pay cards.  Developments are diamonds and cost cards.  Civilian worlds also cost cards; Military worlds are free but require Military pre-requisites.  Some worlds (civ and military) are gray; they don't Produce goods during Produce phase.  Some worlds (civ and military) are shaded in (Lost Species Ark World); they Produce a good during Produce phase.  Some worlds (civ and military) are windfalls (Alpha Centauri): they start off with a good, but do not produce a good unless you have a Produce-on-windfall power.

During Consume phase, you consume as many good as possible thanks to your Consume powers.  If you chose Consume-Trade, you trade a good first, and then do the consumption.  If you chose Consume-x2, you consume all goods for 2x the points.  If you didn't choose Consume, but someone else did, you just Consume normally.  During Produce phase, everyone gets a good on a production world.  If you chose Produce you get one on a windfall.

The main barrier is the iconography describing the bonuses per phase.  But the icons become second nature very quickly.

[yuma]

For those who recommended Lost Cities, how is Keltis (Lost Cities the Boardgame)? And I don't know why I didn't include Kingdom Builder in my original list. Is it pretty similar to Dominion? I think I heard someone compare it to Small World, but in reading over the rules it appeared quite different.

[ftl]

Kingdom Builder is not at all like Dominion.

[Dsell]

Kingdom Builder is not at all like Dominion.

But it IS really awesome. I've never played with 2 players, though.

[ftl]

It works quite well with two players, I've played a lot of 2-player games of Kingdom Builder with my girlfriend.

(Also, based on this thread I just got 7 wonders, played it with a few people, it was a big hit. So that was good.)

[Qvist]

For those who recommended Lost Cities, how is Keltis (Lost Cities the Boardgame)? And I don't know why I didn't include Kingdom Builder in my original list. Is it pretty similar to Dominion? I think I heard someone compare it to Small World, but in reading over the rules it appeared quite different.

Keltis is a similar light weight to Lost Cities, a family game indeed. The bonus tiles are fun and add more tactic/strategy, but shuffle luck can still really screw you up.
Edit: Basically the only big difference are the bonus tiles on the game board and that you can choose what to double and don't need extra cards for that.

[DG]

Board game Lost Cities is sort of ok but it you only need to be stuck with one unplayable hand and you're put off the game permanently.

[Kuildeous]

For those who recommended Lost Cities, how is Keltis (Lost Cities the Boardgame)? And I don't know why I didn't include Kingdom Builder in my original list. Is it pretty similar to Dominion? I think I heard someone compare it to Small World, but in reading over the rules it appeared quite different.

Like ftl said, it's nothing like Dominion. I would say it's not really that similar to Smallworld either.

Kingdom Builder is basically a territory-capture game, but the twist here is that you don't necessarily win for getting the most territory. You gain points for fulfilling certain conditions that change from game to game, and you have to keep those conditions in mind when you capture your territory.

One example is that there is a condition where you get +1 VP for every row that contains one of your buildings. I nearly got the maximum points because I was able to use the ability to take up water spaces (you normally can't) and build a practically vertical line straight up the board. But, someone else could have also gotten that high of a score by just ensuring that all 20 rows had something in them, even if they aren't connected. There are rules, however, that make that scenario unlikely, but it's still possible.

And there are three different scoring conditions, so if you get shut out of building on a lot of rows when that condition is out, then maybe you can make up those points by having the most in a row or the most adjacent to water spaces.

The only thing I would say it has in common with Dominion is that both games have random elements that make each session different, which is a trait shared by many other games.