You would have to have a big trout to make it worthwhile to filet - but, just in case, here is how I do it using a bass as the training aid. You'll need a good, sharp filet knife. I use this type of filet knife. For a larger fish, like a big, fat bass, it's easier to go electric like this one here.
First, slice down to the backbone and cut the bottom to open the fish up.
Remove the entrails and rinse
Slice down towards the tail following the backbone. Just cut through all the ribs. Be careful not to put too much pressure on the backbone as you do not want to cut through it.
Here's another view of the backbone slice
Now, time to remove the bones. This is the critical step. Put the filet down on the board with the scales up. Press down gently to squish the bones against the board. Then, slide the knife along the top of the bones to cut them out. The natural spring tension of the bones will keep them against the board - just a matter of knifing along the top.
Grab the tail and slice from the tail to the top. Slide the knife between the meat and the skin
That's all there is to it. This does take some practice - but works great
. For a larger fish, like a big, fat bass, it's easier to go electric 
