Really, experience points are just a game mechanic, used to incentivize and/or reward certain behaviors
As noted in the passage you quoted, they are meant as rough indicators of the experiences that help a character learn, grow, and improve herself...but any close mapping to how real people learn and grow is tenuous at best.
Would apprenticing with a high level wizard help you master new spells as quickly as shooting orcs with magic missiles day after day? Perhaps, but it wouldn't make for an interesting game incentive.
Some GMs assign XP only (or primarily) for defeating monsters. Others use them to reward clever solutions to problems and/or great roleplaying. In either case, looking too closely reveals that XP are really just a means to incentivize and/or reward certain behaviors.
Pathfinder without XP
As a side note, at least half the Pathfinder (and other 3.x) games I play nowadays don't actually use them; the party just levels up when it fits the story.
In general, I'm a fan of doing away with XP in Pathfinder, but there are downsides to doing so. The main advantages I see of using XP versus simply leveling by GM fiat are:
- XP provides visability which some players will appreciate (e.g. I've accumulated 4226 of the 5000 XP I need to get to the next level), and
- Assigning XP values by the book may avoid arguments with players who think they should certainly have levelled up by now.
Put focus into roleplaying, even if you're watching someone else do it. Focus yourself on what they are saying and doing, even if it's kinda boring, and project your body language and voice while you're acting in-character. Be much less high-intensity when simply describing your bonuses while rolling, or asking someone to pass the chips. This will create natural focus on the roleplaying aspect of the game.
Wherever possible, assume what others are doing is a prompt for in-character roleplaying. DM asks what you do? Turn to someone, and say 'Philius, methinks we should cross that bridge and by Everam and St George, charge those there gnolls with swords in hand. Once we have them subdued, we'll take some answers from them, so we must leave at least some alive! What say you, well-met friend?"
Even if people don't respond in-character, and instead shift it back ooc, roleplaying just happened. Keep doing it and others will soon follow.
Ham It Up
Your character is 'quiet' and 'reasonable' and NOPE. Your character is the hammiest of ham. He's a loud cliche. He is instantly identifiable as the tropes that make him up - and he defines the setting by his very presence. It's unfortunate - but humans love ham. They love it.. a lot. Be something simple and understandable and loud, and they will get with the program really fast.
You can do this by being a masterful actor and roleplayer with any character, even a non-hammy one, but it is easiest with ham, so ham I will advise. Your paladin isn't just a paladin who likes cheese and moonlit walks on the beach - he's SIR GALAHAD THE MIGHTY, SUBDUER OF THE PEASANTS, DEFENDER OF THE WOMENFOLK, AND HIS MOUSTACHE BRISTLES AT THE SLIGHTEST SUGGESTION OF DRAGONS.
'Big' traits tend to focus things on the roleplaying a lot faster. Simpler is easier for the audience to understand.
Find people who will respond to your dramatic offers. When you address people, address them first, so they respond in-character, and then immediately pull other people in. People ignore offers initially, but if something is already rolling, they'll get rolled in with it. Some people will instinctively resist roleplaying offers, for all kinds of reasons - learn to identify them too, and offer to them last, once the roleplaying scene has the most momentum.
Be good at plot
Being able to identify where the adventure is going will let you advance the plot during a roleplaying scene - which both speeds up the adventure and means the time spent on roleplaying won't cause a weak GM to not let you hit the end of it.
Roleplay during combat
'LOOK OUT, FARAMIR! THE GNOLL IS AT YOUR BACK!' 'Galahad charges at the gnoll attacking' moving mini 'faramir, and' rolls dice 'swings at it with his mighty sword.' By including both speech and roleplaying-description in amongst your mechanical actions, you partially negate the disconnect that happens during the mechanics-rich combat portions of sessions. Have to know what you are doing on your turn before your turn rolls around, or anti-roleplayers will complain your roleplaying is slowing things up if you are not clearly doing it faster than anyone else.
Additionally, being good at combat, and giving tactical advice in-character that leads to defeating enemies quickly, will give more time overall for non-combat-constrained roleplaying itself.
Occasionally, roleplay during others' turns - have Galahad shout an encouraging phrase at an opportune moment. This has to be rare, and well-timed, though - an advanced technique.
Be Heroic, or Dastardly
Again, ham. By being heroic, and roleplaying it hard, you make other people who are not roleplaying feel heroic. By being dastardly, and roleplaying it hard, you make other people feel heroic also who are not roleplaying. You're giving them some of your roleplaying energy in a way that feels good for them. Morally grey is, again, a tougher sell. Note this isn't 'good' or 'evil', it's more saturday morning cartoon than that. Snidely Whiplashi, or Dudley DoRight.
Incorporate the GM
Don't just roleplay at fellow players. Roleplay at NPCs. Treat them with importance, and give the GM offers to roleplay right back at you. All of this applies to the GM, too. Getting the GM on-board with roleplaying, especially if you can advance the story while doing so, will be a tremendous boon to your cause.
You're right, by the way. Premade adventures, split up groups, schedules, public venues, this stuff just kills roleplaying and really makes it quite hard - I literally could not design a better system to do so.
But even in those kind of circumstances, I have personally sparked roleplaying in some extremely tough crowds. You won't see a huge improvement - but even the tiniest bit of roleplaying can be a huge welcome to you if you're in a roleplaying drought, and if you play with regularly the same pool of people, you'll find people gravitating to you that appreciate roleplaying, perhaps even to the extent that people will fight to have you in their groups.
Overall, though, the roleplaying will be in many ways a simpler thing than the rare high level roleplaying you can get in a home group.
But it's certainly not impossible.
Just have the courage to keep trying and don't give up.
The D&D Adventurers League DM Pack has the documentation to answer what you're asking, and a whole lot more.
The biggest thing to be aware of is that it has rules that trump the guidance contained in older modules - there is a different table that is used now.
When you earn it, the entire lump (XP, GP, DT) is recorded as a single bundle. When you apply it, the whole bundle must be applied to a single character. Each award is applied individually, and only applies to one character.
As far as logging it goes, as long as it's clear, it's really up to you. Personally, I keep my DM Rewards in an Microsoft Excel workbook. It has columns for where the awards came from, what the amounts were, when I earned them, and most importantly which character I applied them to.
On the character itself, the same rule of thumb applies - as long as it's clear, it's all good. I log mine like an adventure, called "DM Rewards". I put the numbers where I normally do, and have a notes section where I include where the award came from. You can lump multiple rewards into one "DM Rewards" entry, as long as there is no actual play time before and after. Each entry should have a date, indicating when the award was applied, just like one indicating when the module was played.
The other thing you'll find in that package is the DM Quests. These are separate from the basic DM rewards just from running, giving you bonus rewards for things like running particular groups of content, running the same thing more than once, and so on. They modify and/or supplement the DM rewards.
These rewards change each season, so make sure you're always using the right season's version of the guidance on them. This is the biggest reason I keep track of the date I run things - it matters for which season they apply to.