To set up for four players, you lay out the central game board, which serves as a point tracker for the players and a path for Jean de Valette, who's going to walk down the street to see what players are doing, but only when someone plays a Jean de Valette card that prods him along. You shuffle the yellow, blue and green building cards, then lay out thirty of them in six rows as shown in the image below. You then shuffle the yellow, blue and green people cards, and lay out a person of the matching color on each building. Yellow items tend to give victory points, green items tend to give money or resources, and blue items tend to do special things. (With fewer players, you lay out fewer rows of cards.)
On a turn, you play your three cards one a time and do their things. If you pay the cost for a building, you add the card on it to your hand and mark that building as yours. At the end of the game, you'll score points for it, and each turn during the income phase you'll earn something for it: money, resources, points, etc. If Jean de Valette is in the same column as the building you constructed, you get a bonus; if you build something adjacent to another of your buildings, you receive a discount. Later in the game you can use an action to upgrade a building — flipping it to the other side to indicate this — doubling both the point value and the income.
One card in your starting deck allows you to cull cards from your deck to a central discard pile in order to increase your odds of getting the cards you want — but this same card allows you acquire cards from the discard pile, thereby allowing you to grab stuff that others have discarded.
The game enters its final phase when Jean de Valette reaches the end of the street (as he's ready to go cool his heels at home), or when a player has placed all of their building tokens on building cards, or when a player has reached the end of the point tracker for points scored during play. After any of those things happen, each player takes their entire deck and goes through it all one more time, thereby giving you a final chance to use everything that you've acquired over the course of the game, after which you tally points to see who wins an invite to the de Valette home as apprentice par excellence.
That's it! I keep thinking there's more to the game, but Hans im Glück lists a playing time of twenty minutes per player, and that seems accurate as the flow of gameplay is straightforward, with all the twistyness of play coming through the variety of building and people cards in the game (since not all are used each time) and whatever you add to your deck in order to make things happen.
(Please note that some details below might be inaccurate. BGG recorded a video overview at Spielwarenmesse 2017, and I'm reconstructing how to play from memory. I've updated this post since publication to add more images and ideally help clarify the explanation.)