Avoid contact with the myriad types of police. It’s not uncommon for them to bolster their incomes by extracting ‘fines’ from the unaware; you always have the right to insist to be taken to a police station (though we don’t recommend this; if possible try to resolve the problem on the spot) or that the ‘fine’ be paid the legal way, through Sberbank. If you need police assistance (ie you’ve been the victim of a robbery or an assault), go to a station with a local for both language and moral support. Be persistent and patient.
If you are arrested, the police are obliged to inform your embassy or consulate immediately and allow you to communicate with it without delay. You can’t count on the rules being followed, so be polite and respectful towards officials and hopefully things will go far more smoothly for you. In Russian, the phrase ‘I’d like to call my embassy’ is ‘Pozhaluysta, ya khotel by pozvonit v posolstvo moyey strany’.