There are two basic techniques for removing bone from fish, filleting before cooking or removing the meat directly from the bones after cooking. These techniques will work for most round fish however certain fish, such as northern pike, have a bone structure that requires a different approach. full story via helium

1. Descale or skin your fish.
2. Fillet your fish.
3. Boil your fish.

via ehow

pic via about.com

1. To start, you will need to rinse the fish and make sure it's clean.
2. Place the fish sideways on the chopping board and create a cut at the back of its gills, then cut it straight down.
3. Now that you were able to remove the backbones next thing that you have to remove are its ribs and the pin bones.

1. The other way of doing it is by cutting its belly and removing it from the fish. 
2. You could use a fork if you want to make sure you have removed the bones from the meat cleanly.

via howtodothings