Stupid question time I suppose:
Are you using the adventure>fishing option and then left clicking on the water? That starts you fishing.
If your pole isn't fully constructed you'll get a little red error message saying you don't have a fully equipped fishing pole. Left click item, right click pole until it has string, hook, bait/lure, you can right click "unequip" and it will take it apart if you're not sure what you're missing. It must also be in your hands obviously for it to be used.
You have to fish on water that isn't directly touching the shore. A boat is ideal.
As for fish jumping: They stop jumping 1-2 hours after the node dries up. No idea why there's a delay, but it's there. If you fish with bait, the fishing animation will stop after a bit but you won't catch a fish. If you're using bait, you're guarenteed to catch a fish if there are any there. Populated areas tend to be very fished out because it's great INT food.