Addition basically means joining of two digits. In the beginning when child is taught about the addition of digits, it is simply done by forward counting. Suppose we need to add 5 and 3, so we will count 3 digits after 5 to get the result. So it will be 6, 7 and 8. Thus we come to the conclusion, 5 and 3 add up to give 8.
Another method of doing fast addition is by remembering the numbers as pairs.

If we make the child remember that which two digits join together to make the pairs of 5 and 10 respectively, then addition becomes faster. Like (5, 0), (4, 1), (3, 2), they give sum 5. On other hand we say (10, 0), (9, 1), (8, 2), (7, 3), (6, 4) and (5, 5) add together to give 10.

Now when we need to solve 3 digit addition problems, first we will place the digits at their proper place and addition operation is performed. We also need to remember that addition is to be started from ones place and then digits of tens place are added up and then we will add digits at hundred place. Also we need to remember that in case sum is more than 9, then tens place digit is carried over to next place.

Let us take the following example: Add 372 + 126,
Hundred       tens     Ones
3                    7          2
1                   2           6
Sum = 4                    9          8
Same methods can be used to add up the digits in word problems.