A large portion of the village won't move in until you've either filled some sort of requirement or allowed enough time to pass. Here are the requirements to get certain villagers/shops to appear in Flower Bud.
The library will be set up after you visit your first festival. Maria moves in, as well.
Raise Alex's heart level to one and ship 30 herbs (any combination of herbs will do, as long as the total is 30). The Sanatorium will be built above the doctor's office and Dia and Gina will move in along with it.
Place a flower in the shipping bin in the town square before the Flower Festival (Spring 23). Lyla will begin visiting Flower Bud on weekends. Ship a number of flowers, berries, and clay and eventually Lyla will set up shop.
Visit the Horse Race in Spring, where you'll be introduced to Gwen and Doug. Doug will set up his Inn on Summer 1 and Gwen will move in along with him.
If you attended the Horse Race in Spring, Duke will set up his bar on Summer 1. Eve will show up and begin working for him.
After working at the bar over the summer, Carl will set up his cafe on Fall 1. You'll be introduced to Katie the first time you visit it.
Ship one fish and enter Sunny Lake, where you'll be introduced to Ray.
The first time you meet Louis will be at the Fireworks Festival. He'll move into the Junk Shop after it expands.
After shipping your first herb, you'll be introduced to Basil upon entering Sunny Lake.
Once you ship a number of ores, Tai will set up his blacksmith's shop and bring his grandson, Tim, into the village with him.
If you attended the Horse Race in Spring, Ronald will move into the village after you plant your first grape tree.
Meryl, Ronald's niece, will move in after you befriend Ronald.
Saibara will move in after you ship your first piece of clay, which can be dug from the second floor of the cave mines.
You'll meet Terry the first time you enter Sunny Lake.
The first time you'll meet Nami will be during the Swimming Festival. She'll hang around for the rest of the Summer, and all of the Summers thereafter.