Cu + AgNO3 = Cu(NO3)2 +Ag

The problem is that you have to balance Cu + AgNO3 = Cu(NO3)2 + Ag

The first step is to identify all the elements and how many atoms of that element there are on either side of the equals sign.
When you do this you will get,
 
1 Cu 1
 1 Ag 1
 1 N 2
 3 O 6

Next step is to make sure that all the elements are the same on both sides. This is mostly trial and error until you balance both sides. 

The solution to the equation would be:

Cu + 2AgNO3 = Cu(NO3)2 + 2Ag

So now if you check your elements, you will get the following:

1 Cu 1
2 Ag 2
2 N 2
6 O 6

As you can see all the elements are equal on both sides, so the equation is balanced.

Answer is to avoid experimental error