This is a common difficulty to have when using the basic fishing rod, for both the Wii and Gamecube versions of this game.
The short answer: you just need to have a gentle touch with the fishing rod and be patient.
The long answer:
First of all, you have to actually find some fish; you can usually see them in the water.
1a. Using bait on the rod will speed up the process of catching fish, but it is not necessary. Still, if you have some bee larvae on you, there's no reason not to use it.
1b. If you are not trying to catch a particular fish, fishing in a spot with a high concentration of fish will increase the rate at which you are able to catch them.
Throw out the fishing rod towards the fish, so that the bobber lands as near to them as possible. Let the hook sink into the water. To attract their attention, move the fishing rod around very gently, and don't overdo it; just give it a nudge side-to-side or tug it towards you slightly every so often, in little bursts of movement. This isn't entirely necessary to attract the interest of fish (they will eventually become slightly interested in the hook anyway), but it does speed up the process greatly.
If they are near enough, the fish should become interested soon. If you can see them, watch to see when they are approaching. Keep encouraging them by making delicate movements with the rod, and if you see a fish swimming towards the hook eagerly, prepare for them to take a bite.
When a fish bites the hook (the controller/remote will vibrate), then you tug the rod upwards quickly, and you should have hooked the fish. Keep pulling up on the rod to continue pulling in the fish.
The exception to all of this of course is the Reekfish, which you need to catch to proceed with the game. You will not be able to catch a Reekfish without the coral hook you get from the Zora prince.
For a detailed guide to fishing with bobbers, fishing with lures (in Hena's Fishing Pond), and what fish you can catch (and where) in Hyrule, you should refer to this guide.