abax addition fig. 6

 This abax represents the number 278. We are going to add 554 to it. Do you remember how to start? You add the highest columns first. So you would put another 5 pebbles in the hundreds column...

abax addition fig. 7

 ...giving you this. This is the number 778.
 When you look at the next column to the right, you will immediately see that they add up to higher than 9, so that immediately tells you that you will have to carry a 1 into the hundreds column. Do it now. Place another pebble into the hundreds, giving you...

abax addition fig. 8

 ...878.But remember, you only needed to add 5 more in the tens column (which would have been 50) but you added 1 in the hundreds instead. So you have added 50 too much. Simply remove the extra 5 in the tens column now. (That would be the tens-complement of 5, remember?)*
 

abax addition fig. 9

 Once you have subtracted five pebbles from the tens column, you have the above situation, which represents 828.
  You still have to add the last digits together, and when you look at them, you will immediately see that they, too, will add to over 9. So, as you know, you will add another pebble to the tens column now.

abax addition fig. 10

 Once you have added that pebble, you will have the number 838.
 As you also know, you just added 10 (one pebble in the tens column) when you only needed 4. So, to make up for that, you have to subtract the tens-complement of 4 (which is 6) from the ones column. Once you have done that, you will get...

abax addition fig. 11

 ...832, which is the final answer.
 It should be easy to follow this process in these diagrams. It is much easier when you actually have an abax in front of you and you are manipulating the pebbles (or marbles) yourself.