Pair Numbers
Pair numbers for players are normally based on player ratings, and SwissSys handles this for you automatically as long as you have the setting “Sort new players” switched on in the Environment Options dialog (registration and editing tab).
When this option is turned off, players will be assigned pairing numbers in the order in which they are registered.
Automatic Updates
Similarly, if you change a player rating, all pair numbers will be automatically updated as long as the above option is checked.
FIDE Mode Restrictions
Note, however, that if you are running in FIDE mode there are some restrictions. In that case, pair numbers will be changed to reflect late-registered players or rating changes, but only up until the start of the fourth round.
From then on, FIDE rules do not allow any further changes to pair numbers and SwissSys will maintain the same player order even if you add new players or change ratings.
This is important, because FIDE pairings are based on pair number, not rating, even though the two are usually going to give the same order.
Equal Rating Handling
If two players have the same rating, how they are sorted in the pair chart depends on whether you are in FIDE mode or USCF mode. FIDE expects players to be sorted first by rating, then by title, then alphabetically.
For USCF mode the sort is strictly by rating, with equal-rated players being sorted randomly. (If you are in USCF mode you can optionally sort equal-rated on a first-come-first-served basis by unchecking the “Randomize order for equally rated” option in the Environment Options dialog.)