1) Though it is awaiting game as Neko Atsume, what you do is the preps for his trips/packing,with food, travel gears and good luck charms.
2) The currency is clovers which grow in his yard.
3) He travels to many famous vacation sites in Japan and sends cute pics from there or somewhere on the road in between.
4) He brings back some local specialties, including food items and non-food items, as souvenirs and you try to complete them. However,there is no souvenirs if you get him only cheap food, besides the first trip.
5) There are visitors like a snail, a bee and a turtle at his door. Each time they visit, there is a flyer in the mail box, and you get alottery ticket if you view it by tapping on it. Make sure you have an internet connection before you tap, and it will ask you if you like to view the advertisement or not. Then you tap "はい" which is yes.
6) Tap on a visitor, the food souvenirs box opens, which you get from the frog, then you choose the food to treat the visitor with. In return, the visitor sends lots of regular clovers or one four leaf clover later.
7) Time to time,the frog gets the new titles as a traveler, like a care-free wanderer. You can see them by tapping on him, but they are in Japanese. It seems that those titles have some effects on the development of the game.
8) Eventually you start seeing his traveling buddies, a red crab, a mouse & a butterfly,in his photos. They are absolutely adorable!
9) You get lottery tickets from visitors and the frog, usually when he returns. With five of them,you can play it. Go to the shopping page, then tap on the icon on the top right corner to go to the lottery page. Tap まわす to play only if you have five or more tickets. If you get a white ball, that means you lost.
10) You can see the list of goods you can win by tapping 景品一覧. With a yellow ball, you have choice of train tickets with four different directions. With a red ball, you have choice of Konpeito-candies with four different flavors. With a green ball, you have choice of Tamago-boro snacks with five different flavors. With a blue ball, you have choice of good luck charms with five different colors, which are from Shinto shrines, and I assume they are much more powerful than Four leaf clovers. All these can influence his choice of the destinations.