Catching bugs on the island at night
Turnips
Selling villagers or spare items
Perfect fruit
You can sell some gyroids, fossils and do the money rock xD That's what I always do when I start off a game.
And the options Mary listed.
You can sell villagers here on the forums. People can pick up villagers that are in boxes from you, and you can charge them. If they are popular, you could become rich!
The fastest way is to sell turnips and go beetle hunting on the island. IMO, selling villagers takes way too long.