The idea in Trains is that you are a railway company building to connect cities and suburbs. For now they're in Japan, because that's where the designer is from; two hex grid maps for the environs of Tokyo and Osaka are on a double-sided board. You build track to connect those urban areas. Stations the players construct in those urban areas are worth points when you connect them. In order to do these things, you use two core types of cards, around which all else revolves: Rail Building and Station Expansion. There are a few other ways to get points – you can buy the equivalent of Provinces (Skyscrapers), Duchies (Towers), and Estates (Apartments), which go into your deck as deadweight – but these points are marginal in most cases. You can win with a very limited rail-building strategy with extreme card mixes, but for the most part it's about building the stations and rails.
The kicker, and the thing that makes the game hang together in interesting ways, is Waste. Anytime you do any of these things that help you win (build rails, build stations, or buy VP cards) you add one or more Waste to your deck. Waste is just a dead card – it's not worth negative points like a Curse, it doesn't have deleterious effects like a Disease, but it does cramp your style. There aren't many reasonable ways to play the game that won't involve getting rather a lot of Waste into your deck over time. How to manage your Waste is a key strategic choice, ranging from very aggressively trying to get rid of it via the action cards that allow you to recycle or landfill it to ignoring it, trying to counterbalance by purchasing lots of positive cards, and hoping it doesn't hurt you too much.
Waste is what gives Trains its unique feel. With its many expansions Dominion is pretty wide-ranging (I admit I checked out back around Prosperity), but basically it's a game about maximizing your chances of a monster hand you could use to buy expensive but high value-density Provinces. Once your deck started clicking, it accelerated rapidly to the end since the Province cards themselves weren't a significant drag. Because of the stream of Waste in Trains, instead of optimizing for the monster hand you're generally trying to make sure you can do at least something useful as often as possible. Usually that means Rail Laying or Station Expansion plus some cash. You almost always need card combinations to move forward (Rail Laying cards don't come with cash), which makes keeping your deck balanced crucial. When it comes to building rails and stations, cash is key but it's rare you'll need really large ($5+) amounts; but you will need to build a few expensive connections, so you do need to make sure your have that capability. You can do all this the with some amount of Waste in your deck, but beyond a certain point it starts to throttle you, and you need to make sure you don't drown in it. This balancing act is then further complicated and made interesting by the many action cards that allow you to do Dominion-esqe card and deck management.
The other major positive effect of Waste is that it gives the game a pulse, a push-and-pull that is absent from almost all deckbuilders. Because of the nature of card randomness, you'll usually go through bursts of activity which add a lot of Waste to your deck, and need decide whether to ignore it and press ahead, add action cards to your deck to deal with it, or spend time to remove it (you can pass your turn to remove all the Waste in your hand). As Waste is added to and removed from your deck in chunks, and as the randomness of the card flow takes its toll, each deck cycle has a different feel. Sometimes it's about improving efficiency, sometimes it's about building things, sometimes it's a balance, and sometimes it's about powering ahead in the face of declining efficiency. It's not impossible for Dominion to have this feel also with the right card mix; but in Trains, creating this ebb and flow – key to making a narrative game interesting – is an essential element of the design.
There are a number of key things that Trains wisely did not import from Dominion. There are no limits on buys and actions; buy and play as many cards as you want. Getting rid of these inorganic limits makes for more intuitive play, makes lower-cost cards more worthwhile, and gets rid of boring "+ action" and "+ buy" cards. Other than for Waste there is no card removal, so there are no boring deck-pruning strategies and you're simply going to have to deal with eventual deck bloat.
Also gone are attack cards, replaced by the more interesting on-board competition for routes and cities. Track is owned by players but stations are neutral, so there is an incentive to leech off of other players' networks. You can never be blocked from a space, but it costs extra (both in money and Waste to build where someone else already is. There are definitely cooperative-competitive tensions, although I think in general the high costs of building into other players' networks rewards getting there first – it's definitely not impossible to win by building up your own isolated track and station network. As always, though, the mix of cards available for purchase can change the balance between building and leeching somewhat.
Like Dominion, Trains offers you 8 random sets of cards to build your deck from as the game goes on. There are a number of game-changer cards: The Tourist Train can make winning with a small deck, minimal on-board network, and lots of VP cards viable; The Freight Train offers dramatically easier Waste disposal; Collaboration makes building into other players' networks and cities much easier. Because your deck generally has to do more fundamental things (build rails, stations, remove waste, generate cash) than other deck-builders, there seems to be a wider variety of interesting cards for any given situation, and games rarely revolve entirely around one or two big power-cards. Like all of these games, it seems likely that Trains will need expansions to maintain long-term interest once players mine out the balance implications of many cards. That having been said, I think Trains gets great mileage out of it's 30 or so different cards, and is much less susceptible to boring or degenerate mixes. I'm a hardened veteran of deck-building games, and Trains has yet to feel repetitive after 15 plays (Trains is very easy to teach and relatively short at about 45 minutes).
Trains looks like a Dominion ripoff – especially if you just read some card texts – but it most certainly is not. Clearly a lot of thought has gone into how to create a game with a very different texture. Instead of a pure race based on one powerful combo or a couple key cards at the outset, you have to make turn-to-turn and deck cycle-to-cycle decisions based on evolving game state. Instead of a relatively themeless game of interacting card powers, you have a clearly realized theme of building up infrastructure and capabilities in order to expand a physical network. I tend to like deck-building games generally, but Trains really hits a sweet spot for me, and it shows how powerfully a coherent design focus can work to breathe life into a game.