At the beginning, you already have 10 reputation with police.

Ferenz's gang

I think you should know that a bunch of scary looking guys moved into the old industrial plant near the train station. +5 reputation

Guys in the industrial plant are forming a gang. They seem rather determined. +5 reputation

I’d like to give you this dagger. it was used in a hobo murder (get the dagger from Bear hobo, Veiled Vindicator quest) +5 reputation

I found a dead body under the train overpass, In the little park there. It was just buried there. (follow quests from private detective Souček) +5 reputation

Bruno's gang

You can wait with those until you finish the quest line with Bruno, if you report those before, you loose Bruno's reputation.

This Bruno guy asked me to steal bikes. (Anton needs to ask you to steal bikes) +5 reputation

Bruno is blackmailing your colleague Kvapil. (Bruno will eventually ask you to get a dagger taken by police) +10 reputation

Bruno is selling stolen car stereos. (Anton will send you to Bond, he will teach you to steal car radios) +10 reputation

Moiser's gang

There is a drug den on Wenceslas street. They wanted me to help them with distribution.” (sell drugs for Ramsy) +5 reputation

They’re cooking some new drug in that dealer den. They call it Kraken.” (Moiser will tell you about Kraken after finishing the mystery with drug stealing) +5 reputation

Dealers from Wenceslas street gave me this package. I was supposed to deliver it to a dead drop. It’s drugs.” (Moiser will give you a package with Kraken when enough reputation) +30 reputation

In order to obtain Model Citizen achievement, you have to report all of the criminals above (NOTE it sums up to 95%, not 100%!) and talk to the police to receive a medal from them.