Being an Outsider is great! You’re on the Good team, so you’re in the majority. And you have very little responsibility! Basically, you have three jobs.
1) Help account for other Outsiders,
2) Get people to believe you, and
3) Stay alive. This is optional. Unless you’re the Saint.
Ironically, there’s very little point in hiding if you’re the Recluse. Letting Townsfolk know that you can cause their abilities that detect Evil players to work incorrectly may help you build trust. You may want to locate a Fortune Teller to let them know they will probably get a false positive on you so they can focus elsewhere. (Remember, you might register as evil, but you also might not!) Find out if you neighbor an Empath, so they know as well. A Ravenkeeper or Undertaker will want to be aware that if they check you it will likely yield incorrect information. (You might want to either seek them out privately or make a vague announcement to Town rather than ask if anyone is claiming that role. Asking players to out their role in public doesn’t help you build trust, and could make them a high-profile target for the demon to kill!) Building trust is key, since Recluse is an easy bluff for Evil players as it lets them explain away why there is an Evil ping on them.
If you’re the Saint, your first job is to not get executed. You can play it very openly right from the start, and that’s an excellent plan, but don’t be surprised if people are skeptical. Like Recluse, Saint is a frequent bluff for the Evil team, since Town is unlikely to execute the Saint until they have exhausted most or all other possibilities. So you may choose, instead, to hide. You could ask in Town Square that if there’s a Ravenkeeper who gets a chance, they should check you to prove that your very important and useful role as the Empath/Fortune Teller/Monk/other valuable Townsfolk role is proven. Obviously you’re none of those things, but it might bait the demon into killing you at night, which is great. (Remember, dying at night is not the same as being executed, and you can’t be executed, but dying at night helps people trust you.) And if there actually is a Ravenkeeper who checks you, then they can back up your story! But don’t be surprised if the Evil team start trying to frame you (and everyone who trusts you) once people know you’re the Saint. So once again, building the trust of at least some of the other players is important.
The Butler is probably the most underrated, and certainly the most maligned, Outsider in Trouble Brewing. Many people see it as useless since you don’t get to vote unless your master does, but it’s anything but useless! You may want to pick someone to your right as your master so you can see if they are voting and prepare accordingly. Or you may want to pick someone to your left, so if they drop their hand at the last moment you aren’t on the hook for voting without them. (A good Storyteller will count your vote if it appears you voted in good conscience, believing your master was voting too, but they dropped their hand late.) Most importantly, you have the ability to make and break alliances. If you find a master you trust, you have a powerful (albeit small) voting bloc. And if they’re refusing to vote on people you have good reason to believe are Evil, you can always select a new master and call out your old master to Town. You can let someone know they’re your master and ask them to vote on people. They may be more likely to listen to your arguments if they know they are your master. Or you can not tell them, and slyly watch who they’re voting on and see if you agree, or if you think they’re Evil and trying to frame someone. You can even tell one person they’re your master when someone else actually is, just to muddy the waters and see who will turn on each other.
One of the most important things Outsiders can do is help account for their numbers. The number of players determines the number of Outsiders that are in play. If there should only be one Outsider, and you and exactly one other person are claiming to be Outsiders, either the other person’s lying or there is a Baron in play. If there is a Baron in this game, there must be a Drunk somewhere, in which case Town should be aware that someone’s info might not add up. And if it’s a smaller game (7-9 players) there will only be one minion, and now you know which one is in play! So there’s no need to worry about a Poisoner, Spy, or Scarlet Woman.
If you’re either the Recluse or the Butler and you’re nominated for execution, recognize that your best reason to stay alive is so you can keep voting. But that’s only worth so much. If Town don’t believe you and it looks better to close the possibility that you aren’t trustworthy, it’s probably worth it to accept your fate. Remember, you still get a vote, and if you’re the Butler you are no longer bound by the opinions of anyone else!
You can also ask the Storyteller for advice or refer to the official Blood on the Clocktower Wiki for more tips. And above all, remember it’s just a game, and if you lose, that just means it’s time to play again!