What's the most efficient way to earn Rupees early on in Zelda: Skyward Sword?
Solution 1:
At the point you're at, you don't actually need all the shiny stuff right away. The Bug Net and the Extra Wallets are probably what you need the most right now, especially if you want to buy the shinier things early.
That said, this early on, there are few ways to get Rupees effectively:
You can try to find all the Goddess Cubes you can and open them; they can contain Rupees, but often contain other things.
You can catch as many bugs as you can with the Bug Net (Deku Hornets come in especially large numbers) and go see Stritch in his room at the Academy at night. He will buy some bugs off your hands, but only buys four specific kinds of bugs a night.
It is doubtful you have a lot of treasure by now, but if you're willing to part with them (keep in mind they are used to upgrade your equipment at Gonzo's), Rupin will buy treasure from his house at night on a mechanic like Stritch's. His house is located on the other side of the river, near the graveyard.
There is also the classic "break everything you can" strategy. Break all the pots and skulls you find. Cut all the grass and flowers you can. Roll into every tree.
Solution 2:
One other thing that you can do for some (relatively) quick rupees early in the game is sky-dive down to the Pumpkin Landing (the island with the Lumpy Pumpkin on it) from a high altitude.
On your map, set your beacon on Pumpkin Landing and then fly towards the column of light that your beacon gives off. All the while, fly higher and higher. Once you start to get close to the Lumpy Pumpkin keep checking your position on the map (it helps to zoom in), and when you're over top of the Lumpy Pumpkin dive off of your bird. On the way down you'll see these multicolored flying squirrels, if you can touch all of them before you land/use the sailcloth then you'll get 20 rupees.
You can sky-dive successfully if you're just at the top of the column of light that your beacon gives off, but it's easier if you're as high as you can go when you dive off of your bird.
Solution 3:
At that specific moment in the game, the best thing you can do is to use the Beetle (your flying bug remote) in the large dome room surrounding the room that you got the Beetle in.
There are several boxes hanging from the ceiling, use the bug remote to cut them down, most have a red rupee (20 rupees) in them.
Also look around the top edge of the room, there are lots of little crevices all around the edge of that room that contain rupees as well.