Attractions are the cornerstone of your success. To build them, you need to have money and attraction cards.
Find a place with a + sign to begin your construction:

When you click the cross, you will find a selection of available attractions:

Choose the building you have enough money and cards to build, then click the green button with the price. The construction will start right away.

Note that you can have only one construction going at a time, so you might consider speeding up the process. You can do so by paying gems or watching ads. Using gems will finish the process instantly; watching videos will minimize only a fraction of time.

Star construction site grants you the most fun attractions.