You'll have to beat me a few times and give me some pointers. I played the tutorial then got lost very quickly in a game vs. the AI.
Yeah it's actually pretty simple even though it's known as a heavier game. Let me just go off the top of my head to see if it helps the game make sense.
On your turn you do two things:
-Supply (add to the offer piles at the bottom based on the tile you just went on (these are hidden first round then stay the same the rest of the game)
-Main action, which is either:
(1) Grab everything on a single offer pile, usually a a bunch of wood or clay or whatever.
(2) Use a building by placing (or moving) your disc. You can use either the "city" buildings, which belong to the game and get added to as the game progresses (top right set of buildings) or player's buildings, which belong to players but you can use freely. This is where the UI is not so great -- you actually have to tap in to see peoples' buildings otherwise you just see the names. It's not THAT bad though but you do have to be aware that all bought/built buildings are available to you (unless they have someone else's disc on them). These buildings let you do a TON of different crap, from building other buildings to getting resources to upgrading resources. NB: Many buildings require you to pay an entry fee -- top right -- usually francs or food. Note that francs can always be used as food but not vice versa.
You can also always BUY or SELL a building by paying its cost, which is usually the same as its value but sometimes more. This is pretty clear from the card. Buy/sell is a free action and does not take your main action.
End of game you add up all your francs (which are basically VPs), buildings, and bonuses, and subtract any loans and highest value wins. Normal game flow is to buy a few good buildings, buy some ships here and there (these help you meet your food needs every round), and then maybe amass some goods to use with your ships at the end of the game when you use the Shipping Line building.
It's all a bit murky until you play it a couple times, then it's really easy. Actually easier than Agricola in terms of mechanics as well as greater freedom of action (unless you get some cheap cards or have bad opponents, Agricola is really a game about minimizing pain whereas Le Havre is more about maximizing profit if that makes sense).