Priority 0: Shoot liars. Some players still try and spin these stupid fairy tales saying that lying helps the town. They also believe Voldemort is real. Don't listen to them. Without going in depth about why lying is bad just follow this statement - SHOOT first. There are very few instances where lying benefits the town. Even then it usually ends up benefiting the Mafia much more. When players sign up for a game in which they know multiple people playing aren't stupid enough to let all their lies go unpunished they have to step their game up considerably. Look at all the terrible games that are littered around this forum. You want to know a recurring theme? Townies lying trying to make a hero play, and then Scum lying since that is now the temporary "way to look town". Shoot before it hits LYLO with 3 people that have roles that can't be confirmed. In fact shoot them because when a player lies about being a Cop and the real Cop gets night killed or lynched the game is essentially over. DONT LET IT GET TO THIS POINT. EVER. Nothing sucks more than an end game scenario with tons of WIFOM.
Priority 1: Shoot people that are talking nonsense. Activity doesn't make someone pro-town. You shoot people that are saying one thing but doing another. This goes especially for people using meta arguments that do things scummy regardless of alignment. Shoot them Night 1 if the rules allow it. Along with this shoot players that will help untie clashing role claims, or clashing scenarios. If you're in a situation where the death of one player confirms something about another, shoot. Most players are braindead anyway and this is one of the few times where it helps to take matters into your own hands.
Priority 2: Shoot lurkers
This is almost a priority 0 but people that play Scummy are always best shot first. However, shooting lurkers establishes an awesome town meta. If people know other players won't stand for their inactivity, and the threat of a modkill leads to a ban they wont sign up. Likewise like I said in countless mafia games in the past: people that are defending themselves are much more likely to be valuable than people that don't. So shoot the people that lurk when called out all the time, and shoot the people that won't contribute after repeated prodding. They are USELESS to the town - kill them before it hits LYLO. You'll be sorry if it does.
Priority 3: Dont shoot
If none of the above apply then by all means - hold your shot until more information is available. Also some people say "dont shoot players that are going to be lynched the next day" but this isn't good advice. Anything can happen to turn a lynch around. You yourself might not even be around to shoot again the next night. If someone is almost universally considered scum - shoot them that night. The town now has a new set of suspects to discuss.
Don't claim unless you have to. This goes without saying. Either claim near LYLO and explain the past kills, or claim without shooting and then say you're going to shoot a confirmed scum that night. Clearly, don't do this if there is a Roleblocker (possibly the best Mafia role) or a Scum Doctor. If there is a Serial Killer in the game be EXTRA careful about claiming. As they are usually bulletproof they will be more than happy to let you kill people and avoid killing you as long as it ends up being a balance between Town and Scum. Also remember that SKs like to claim Vigilante too.
Playing this role is a little bit harder since there are so many variables that go into who to investigate. In general, your best bet is to investigate the scummiest person but even that isn't going to always be a winning play. Unlike the Vigi stuff there aren't many priorities for Detectives since at any time one thing can be better than another. I'm going to keep this short since the best way to play Cop is to get the role, or read a game where a Cop sets up investigations ahead of time and nails Scum.
1.) If an innocent is lynched, depending on the nature of the lynch check someone on the wagon
For some reason this is a play I rarely see being made. In small and medium sized games you should be checking out the players who led the wagon to an innocent lynch. Especially if this is one of those notorious "people just hopped on a wagon that was stupid" lynches. This way you'll know if it was a scum led lynch, or a townie that has no clue what he/she is doing and is best avoided for critical parts of the game.
2.) Don't investigate scummy people that are almost surely going to be lynched
The reason for this is that if there is a Vigilante in the game, chances are they will shoot them. Don't waste your night. Investigate other scummy people that are off the radar of the town.
3.) Don't claim.
Never, ever, ever claim Cop unless it's LYLO or shit has really hit the fan. This used to be one of the easiest ways to catch Scum because competent cops would never claim. Even if you are about to be lynched DO NOT CLAIM. The best way to avoid being lynched is to talk your way out of it. If you claim, the town believes you, and you live guess what? It's WIFOM time. The town will start talking about all kinds of useless shit like whether or not the Mafia will kill you and what Medics need to do but...guess what? The Mafia has a role blocker. You've screwed yourself out of a Night, someone, and hopefully not the Medic will die and now the next Day the WIFOM circle starts again. Don't claim even at the point of death. If you die you hopefully breadcrumbed your investigations anyway.
Don't counter claim Scum unless you seriously have no other way to stop an innocent lynch. Unlike yourself dying and flipping Cop, when a Scum claims Cop and the innocent that gets lynched flips innocent the next bet is usually the "oh shit guess I'm an insane Cop or someone tampered with my investigation". Stop it before it gets there. This could even be Scum trying to bus his teammate. However if you are sure there is only one Cop in the game talk the town out of the lynch. Bring up the "why dont we lynch you to confirm your investigations?" point. Check the reaction, and most importantly the reaction of other players (find his scum buddies, separate them for the gullible townies). As with all things this is situational, but the general idea is that persuasion is your best weapon. However instead of being a Vanilla townie, you've got more information than you think. Use it wisely.
4.) In games with small numbers of Scum - reveal information asap
Once again very situational. But the idea here is that waiting to get 2 Scum investigations off isn't usually a smart play. Unless you are sure your bread crumbs are solid and will be read, just out right reveal your investigation. Even if the town lynches you since it happened so early, the Vigilante will NK the Scum, and the townies will pick apart the arguments about who vouched for your claim and who didn't. Trading yourself 1 for 1 for Scum isn't usually a good idea and thats why this is very situational. If you've got a Scum read on a player that is going to be hard to get lynched then reveal asap. No need to beat around the bush here. If it's for the Scum that play stupid, then by all means take the chance but breadcrumb first. Don't forget to also reveal who you investigated and found innocent. Confirmed innocents are the bane of all Scum teams everywhere. Especially if they live to LYLO.
I'm tired of writing so I'll stop here. The recent play of Town has been so bad that something needed to be said. This has nothing to do with the being new/newbie - some people that have played multiple games still do incredibly bad things as town. Unfortunately this bad play can end up screwing their pro town roles like Vigilantes and Cops over since they can't make a logical decision. Then there are some people who get a little crazy as Vigilante like shooting non-scummy players just because they MIGHT be scum and it would be a hero play, or shooting a guy that lead a wagon on Scum and claiming it was a bus. Possible but the chances are low that happens anyway. Cops that investigate lynch bait usually need a stern talking to as it's just a waste of a night.