I confess that, when my cash flow situation leave me with no beer money, I resort to acting as a Gypsy cabbie. Here are a few comments from the driver's point of view.
Passengers from among the locals are less hassle. A local knows exactly where he/she is going and give me the nearest generally known point (major highway, intersection, or Metro station). A local client will often name his own price thus sparing me the need to think. Moscow clients know the road/traffic situation and will understand if I don't get them right to their doorsteps.
Foreigners, on the other hand, will usually require me to know exactly where to go. They will impose on me the task of figuring out the rate. They will often assume that I will want to take advantage over them and will bargain aggressively. They will not be happy if I let them off on the other side of the road from where they want to get to. Often they will not even be able to clearly name the address.
Giving a ride to a local is a diversion; doing same for someone fresh to Moscow often resembles work.
If you want lower rates act like a Muscovite. No need to hide that fact that you are a foreigner. Just know where you are going to. Give the nearest generally-known point, eg. the metro station. Don't insist that the driver makes a U-turn just to get you right to your destination.
But the main thing of course is NAME YOUR PRICE AND TRY TO GET IT RIGHT. 100 roubles for a short ride, 300-400 half-way across the city, 600 to the other end of Moscow.
Oh, another thing a local will do is try to pick a car from the flow of traffic going in the desired direction so the driver will not have to go much out of his way. So just about any price you name will be acceptable.
Avoid "professional" drivers. Pay in the beginning to avoid misunderstandings or scam. There are lots of cars in Moscow with owners not having any cash to fill them. Once you get the pattern it should be quite easy to get a ride at a farily low price. No more than an equivalent of $1/km..
Hope the above helps.
Pasha
www.unclepasha.com