Each digit lines up into columns.
We start with the right most column, where 5+7=12.
Since 12 has more than one digit, the 1 in the tens place is "carried over" to the next column.
The addition continues left. Since there is a carry over from the last column, we have to add it to this column's sum.
The sum of 1+6+3 is 10. Since each column only has one digit each, it is necessary to carry over again.
The sum final sum.