To discuss market making, it is important to understand what they were traditionally as well as what they have become.
Traditional Market Making
Traditionally, the profession of market making was designed to 'prop up' the liquidity of the marketplace throughout the trading cycle when there is not enough "natural" liquidity to keep prices efficient and accurate.
In return, market makers would be allowed to take a 'spread'. This means that they are allowed to 'Buy Low' (Bid) and 'Sell High' (Ask) at the same time and make a profit based solely on that spread. In the strictest sense, market making is not about taking directional positions - they make no assumption of where the market is going. Instead, they are only worried about the likelihood of a stock moving against them before they can exit a position (which is a risk that is compensated by the spread).
You, as a retail investor (as well as any institution that is taking liquidity for a directional position), will be doing the opposite. If you want to buy a stock, you must do so at the Ask and if you wish to sell a stock, you must do so at the bid.
I could go on for awhile about the implications of this system, but I think that is the gist.
Market Making Today
Today, market making has become much less defined and more complex. Instead of a strictly 'sell-side' affair, market making has become part of the strategy of many institutional strategies.
High-frequency trading, which another poster mentioned, very much evolved out of market making. Price manipulation is a slight misnomer for how HFT market making might affect your trades - it really should not affect your positions in the long term.
If you are looking at the markets as a long or even medium term investors, market-making & HFT will not have an affect on the fundamentals of what makes your trade a good trade. More often than not, the existence of those participants will actually help you execute your trade as well as get the most accurate price.
Sorry if I just confused you more - this stuff is not all that complicated but it can seem very daunting when starting out. It is mostly just jargon and once you are in the industry for a few years it becomes second nature -
To answer your original question
How often is it a market maker? 100% of the time. When you (as a retail investor) buy a security, you are "taking liquidity" which means that you are buying from someone who has "posted liquidity" which is another way of saying market maker.
Hi Ray, in terms of market making, the stock market and the options market is actually very similar. If you hop on your TD Ameritrade account and buy a stock or an option, you will almost certainly be buying it from a market maker (or your broker will at least source it from a market maker for you). To illustrate, check out the links at the bottom of this that I just took of a trading platform. In the first one, you see some of the current options (Calls and Puts) on SPY that expire in January. As you can see, it lists the Bid and Ask price of each, just like I was talking about in my post. Above, you see the "Underlying" Big and Ask price which represents the Market Maker's pricing for stocks. If you want to Buy a stock on this platform (which is a retail trading platform), you must buy at the As and sell at the bid for both stocks and options. This is known as "taking liquidity", which is the opposite of market making which is "providing liquidity". In the second picture you see the "Depth of Book" of SPY. This shows all of the market making activity at price levels which are "deeper" than the top of book Bid and Ask Price. Although options do have market makers aside from those at the top of book, options depth of book doesn't really exist. I hope that was helpful!
Update: Market Order / Limit Order
As pointed out below, it's worth noting that my above answer only took into consideration market orders - if you do a limit order you may be adding liquidity as well.
I still stand behind my conclusion though - if you are providing liquidity through a limit order that is not top-of-book, then you are effectively a market maker (even if that wasn't your intention). Therefore, when you take liquidity, you are interacting with a market maker.