First, some general tips:

Dont role claim unless necessary there may not be a doc!

Dont be overly aggressive before you role claim. You dont want to draw any more attention to yourself than a townie does. But in the same light, don't be a wall flower. Lack of participation may be a tip off to the mafia that you have a power role and are trying to avoid attention.

Don't ever, ever, ever, ever mention the cop in passing. "Well the cop should probably..." is a dead giveaway that the person is a cop. This is my most reliable method for finding the cop when I am mafia. Its amazing how often a cop will say something like this. thanks, AmertitecTech

In general, you should avoid lying about your role.

Now on to some specific play:

Day 1 dont be afraid to vote against someone. You have no information, neither does anyone else, dont look for concrete reasons: there are none. Being too timid with your vote is something the mafia is looking for.

Night 1 I would investigate someone who has participated less. Mafia may be trying to fly under the radar, also, someone who is talking more is more likely to be caught by discerning townsfolk. Go after the quiet ones.

Day 2 You either got a pro-town result or found your first mafia member.

If you got a mafia member, go back to day one and see if he/she slipped up anywhere (it will be easier to tell now that you know for sure that he/she is bad). Vote against him/her using the information you found from day one that made you suspicious of him/her. Do not reveal you are the cop if you can get the town to lynch without the extra weight of a cop role claim.

If you found a pro-town member, dont worry. 2 people are dead now, leaving only 5. You know 2 are good (you and whoever you investigated), leaving you a 2 in 3 chance of voting against a bad guy. Again dont be shy in your vote.

Day 3 if you made it to day 3 the town must have lynched a bad guy. Time to role claim! Share everything you know up to this point. Who is good/who is bad. This coupled with the voting history should be enough to figure out the remaining mafia member.