First, there are some general principles one should be aware of regarding market makers:
- The exchange usually gives them incentives to provide liquidity (in options markets, rebates have actually been extended to the average joe if someone hits your limit).
- The market maker doesn't (shouldn't) care about market direction.
- The market maker makes a profit off of roundtrips of their limit orders, someone buying their ask then selling into their lower bid and vice versa.
If a security has been trading, it's easy for a new market maker to come in and post orders. Most of it's now computer generated, so the computer will look at the last trade or the mid-point of the bid/ask and post its' own bid & ask and adjust them accordingly once one of the MM's orders is filled.
If an ask is hit, they will continue to post asks but at much higher prices because they will be overloaded with shorts. They will take into account the volume and try to make some sort of estimate of how wide the spread they offer should be, X. They will post a bid at (1-X)*ask. If their asks continue to get hit, they will take the average price of all sales and multiply them by that X thus moving up their bid albeit at a much slower rate than their asks since they are becoming overloaded with shorts.
Except for pink sheets and otcbbs, this process is well-handled in advance for the market maker in the form of IPOs where many auctions leading up to the listing take place for the market makers to analyze.
For short-dated options, the MMs typically try to latch on to the implied volatility of the mid-point of their bids & asks to the historical volatility over the same period.
It goes on and on from there, but those are the basics. Reality is a little different because volume typically rushes from one side to the other, and the MMs try to accommodate for fear of losing business or being kicked off the exchange. For options, the only real fear MMs have are sudden moves in the underlying more than the IV they've accepted that hasn't been priced to absorb that kind of move.
Also, just to clarify, the MMs do not determine the prices of the securities. They are only half of the equation when they actually trade. In highly liquid assets, it could just as easily be speculator to speculator, and if the MMs are not posting prices that anyone wants to hit, they aren't trading at all.