J11 should go like this.
|02 04 06 08 10|
|01 03 05 07 09|
J9 and 13 on this side
In all cases (where the board engineer actually bothered to do it) pin 1 on a connector will have a pad that is different than the others, usually it is square as opposed to round or oval. Also, the numbering almost always works out like the above because these connectors are usually used with ribbon cable connectors. Ribbon cable lines are numbered sequentially (left to right or right to left, depending on which way you are looking at it, that's what alignment pins are for). If you think about how those lines connect to the header, the only way for them to do so without crossing over and being a PITA is to take alternate rows on a double row header.
If on the other hand, you are looking for the pin functions, take a look at bigbirds site, he has a lovely PDF which has the RS232 level converter as well as the pinout for the header.