Start reading on this topic, and thre are lots of "rules".
There area two main styles: American and European/Continental.
The American custom is to use the three utensils primarily with the right hand. To cut foods there is a switching of the hands so that the knife is used by the right hand or the hand with which you write. When cutting, turn the tines of the fork so they point down. When finished cutting, set the knife down on the plate, transfer the fork to the right hand, and continue to eat.
The European, or Continental style does not involve the switching of hands. Don't be fooled by its name. This is very common in North America. Just hold the fork in the left hand and use for eating. To cut food the fork is used exactly as in the American style but with no switch of hands and taken up to the mouth with the the tines facing down. Regardless of which style is used to operate fork and knife, it is important never to cut more than one or two bites at one time.
Off the table. Once the utensil is used, it does not touch the surface of the table again!
Soup bowls on plates. The soup spoon would be placed on the plate not left in the bowl.
If passing your plate for a second helping... always a good sign the dinner is going great... place the fork and knife parallel to each other on the right side of the plate. This leaves room for the food.
When finished you give the sign by placing your fork and knife parallel to each other, horizontally across the center of the plate. This can also be in a diagonal. In any case the handles point to the right and the cutting edge of the knife faces toward the diner. The tines of the fork, can be up or down.