Giles: A, a Slayer slays, a Watcher--
Giles: Yes. No! (sets down the books) He, he trains her, he, he, he prepares her--
Buffy: You're Watchers. Without a Slayer, you're pretty much just watchin' Masterpiece Theatre. You can't stop Glory. You can't do anything with the information you have except maybe publish it in the "Everyone Thinks We're Insane-O's Home Journal."
In short, a watcher is a member of the watcher's council, who trains, prepares and guides a slayer, they are meaningless without the slayer, it's the slayer that gives them purpose. You're not a watcher cause your class says you are or you say you are or you have the researching stat, you might be an agent of the watcher's council but unless you're involved in the training and preparation of slayers you're not a watcher.
The first thing you got to do is know what you're talking about, this means know the show reasonably well, I can't count how many watcher's histories have them enrolling in the academy at 18, when 'spin the bottle' clearly shows Wesley is already in the academy at 16. Secondly, read the background story, help story. This shows that the council has been fragmented, meaning there is no official council. This means several things, firstly, there's no way to prove if someone is or is not a real watcher, secondly, it's impossible to RP being some other watcher's boss, or having orders for them or any of that kind of nonsense.
Ok so if you can get past that, the next thing you're going to have to do is find Slayers, stupid things done in this arena are usually, grabbing the first slayer you find, deciding to be the watcher of some OOC friend of yours, or sitting back and letting slayers come to you. Remember the watchers need the slayers, not the other way around. Reasonably a watcher would probably attempt to train every slayer they could, they'd especially try to train the really powerful slayers as those're the ones who're most likely to actually be able to save the world etc with their help.
When it comes to getting a slayer, if they're a decent one you're going to need to court them a bit any slayer that's just like, yeah sure strange person tell me what to do is not likely to be particularly effective on account of being kind of stupid. Remember you can't prove you're a watcher and even if you could there are rogue watchers or even incompetent ones, so to get a decent slayer or to get one to trust you you're going to have to prove yourself. How good a slayer is is going to be roughly proportional to how hard they are to get.
A lot of watchers just want to roll a watcher and start bossing slayers around, but the ordering part of being a watcher is really far less important than the teaching part and as previously said no decent slayer is going to take your orders anyway unless you've shown you're super smart, and even then you have no way to force them to follow orders, your job is much more guiding them than ordering them.
You're a support character, your main tasks are going to be training, finding out information and planning. Finding out information is the best way to start to build a relationship with a slayer, research everyone you can and make notes, possible strengths and weaknesses, research every event and find out the advanced desc if you can, talk to lots of people to find out gossip or find out about their personalities, snoop around to find out useful information, then present it to your slayer, this person is trying to eclipse the sun, they have strong feelings for this vampire and could be lured into a trap so we can stop them by threatening this person. You should obviously keep this up beyond just the courtship phase but it's a great way to show that you know what you're doing, you have something to contribute and you're not an idiot.
When it comes to training it can take more or less three forms, practical: Like sparing with someone and giving advice on how do to things better, or grouping with someone and giving tips on how to do it better, pretty much depends on you knowing the game better than them. Purely RPed, like sessions with them on a punching bag, or one time a watcher of mine taught Keeley Tai Chi, it's just RP but still worthwhile. Theoretical: For instance one time a watcher of mine posed the problem to his slayers that their friend has been kidnapped by a vampire who's demanding they show up unarmed at a certain factory of the friend dies, and challenged them to come up with the best solutions. A mix of all three is good, grouping up and levelling with someone, while not bad really doesn't count as you training them.
A watcher/Slayer relationship is much like a doctor/patient, shrink/client, teacher/student relationship in that you absolutely cannot have sex with them. There are professional boundaries involved, the hardest part of being a watcher is that you're always in the shadows, if you do the character well you can make your slayer/s much more effective and powerful, but you'll never get to be the hero yourself. The biggest problem with playing a watcher is that it's hard, you've got to put a lot of effort into knowing a lot being able to contribute with brains rather than just levelling and whacking stuff, you've got to try to get the good slayers and find ways to help them beyond grouping up you've got to avoid sleeping with them or hitting them, that's probably why so many people just fall to the I'm a watcher now do what I say and sleep with me kind of crap.