Step 1
165
+237

Each digit lines up into columns.

Step 2
165
+237

We start with the right most column, where 5+7=12.

Step 3
165
+237
2

Since 12 has more than one digit, the 1 in the tens place is "carried over" to the next column.

Step 4
1 
165
+237
2

The addition continues left. Since there is a carry over from the last column, we have to add it to this column's sum.

Step 5
1
165
+237
02

The sum of 1+6+3 is 10. Since each column only has one digit each, it is necessary to carry over again.

Step 6
1
165
+237
02

Step 7
11 
165
+237
402

The sum final sum.