The addition algorithm is a series of steps we use to add numbers that are too difficult to add mentally. In the early years of school students will practise this method with quite simple numbers, but at this level the expectation is that students can deal with numbers with almost any number of digits.
As a procedure, the standard algorithm works if you follow these steps:

1. Align the digits in the numbers into columns according to place value. This is to ensure that like terms are added.
2. Draw a line under the last number you are adding and put a + to note which operation you are performing.
3. Starting from the rightmost column and working from right to left, perform the following sub-procedure for each column:
• Add the digits in the column, including any carry digits.
• Write the units digit of your answer in the same column, but under the line.
• Make a note of any carry digits in the next column to the left.

For example:

 1 9 5 2 3 4 + $$^11$$ $$^19$$ $$^11$$ 4 2 3 4 3