The column method is used to add decimal numbers. First, the numbers are lined up with the decimal points aligned. Then each column is added separately, carrying numbers to the next column as needed. For the example of adding 3.77 and 4.28, the hundreds column is added first (7 + 8 = 15, writing the 5 and carrying the 1). Then the tens column is added (7 + 2 + 1 = 10, writing 0 and carrying 1). Finally, the ones column is added (3 + 4 + 1 = 8). The total is 8.05 + 1 = 8.08.