Nicely set tables, whether it is formal or informal dining usually have a tablecloth or placemat's.  To ensure that the linens stay clean once utensils have been used, they should never touch the table after they have been picked up.

So....where do they go?

Picture your plate as a clock

AMERICAN STYLE DINING

When you are eating American style and resting between bites the knife goes at the one o'clock position with the blade facing inward and the fork at the four o'clock position. 
When you are finished eating the fork and knife are placed at the
 four & five o'clock position.

CONTINENTAL STYLE DINING

When eating Continental style and resting between bites the knife is placed with the blade facing inward at the four 'o clock position and the fork is placed at the seven o'clock position.  When finished, the knife and fork are placed at the four & five o'clock position.  The fork tines can be placed either up or down on your plate.

When eating in a restaurant, these positions are silent signals to tell the waiter that you are resting from your meal and when your are finished eating.  Make sure you don't mix up your utensil placement, you could find your meal whisked away!