1) They get the XP from the encounter, usually that is based on the creatures they fight or the trap they bypassed. So, a CR2 creature would give 600 XP total for the group. CRB p.398. Divide that by the number of people in the group, and that gives you the individual award of XP for an encounter.
2) They get time based XP from the
wiki table for the number of days they have played in an adventure. This table ensures that characters do progress, even if the game slows or stalls.
Add those two together, and compare them to the fast track table in the CRB on page 30. When the characters get to 1,300 XP, they are eligible to level to second level. That is done after they complete the current fight they are in, which may take a few more days to finish off. The time counter for the next level starts at they day they earned eligibility, not the day they actually did the wiki changes. The combination of the two sources of XP gets a character leveling about once every 6 months in a slow campaign, and about every 3-4 months in a fast one.
Rinse and repeat for GP earned. If you need any help with the number crunching, just ask. If you have a relatively recent version of eXcel, Mowgli has posted in one of the stickies an excel table that will help quite a bit in tracking the XP.
Next question: Taking a CR 5 creature down to CR 1. That is kind of hard to do, since they are so drastically different. There is the "Young" template that will add several penalties to a creature and bring it down 1 CR level. But after that, nothing that I know of. I have seen "injured" templates used before where the creature starts with only 1/2 its hit points, but it is not really a fair one, as the AC and saves are still at the higher level, and usually difficult for a party to achieve. An owlbear at half his hitpoints is still an owlbear. And and ticked off one too. So, one level is possible, several not likely. Ask your supervising judge for a final say and suggestions.
LPF characters level a lot faster than normal ones due to the time based XP. A PFS scenario used for an LPF game will usually give the characters about 1.2 levels. But, in a PFS environment, it is only 0.33 levels. The first level module, Crypt of Flame, where characters usually exit at 2nd level, had our characters exiting at 5th level. That said, your CR 5 creature may be appropriate at the end of a longer adventure just because the characters have advanced quickly.
Ninja'd by GE, but hitting the post button anyways.