ω-3 and ω-6 Fatty Acid and Inflammation: Prostaglandins
Prostaglandins are short-range hormones that are used in a great many different body tissues to regulate a great many things. Among these is inflammation. Inflammation can be good, as in the swelling that follows an injury, which is a good "natural splint" that helps immobilize the injured region. Inflammation can also be bad, when our response to environmental conditions leads to chronic inflammatory diseases like asthma, or to more serious inflammatory diseases like rheumatoid arthritis.
What are these hormones, and how are they made?
The diagram below illustrates the basic process, beginning with a phospholipid. Normally, phosopholipids are in the cell membrane. Certain enzymes can cut the phospholipid, however, and release free fatty acids. One such fatty acid is used to build the family of prostaglandins and related inflammatory signaling molecules (such as leukotrienes). The "normal" family of prostaglandins is produced from an ω-6 fatty acid. These are typically reffered to as the "series 2" prostaglandins, because in their end form, they contain two double bonds.

Supplementation of the diet with adequate amounts of ω-3 fatty acids makes it possible for cells to use these fatty acids instead, and produce a set of these hormones called the "3-series." These have a third double bond (derived from the ω-3 double bond of the original fatty acid, highlighted above in yellow.
The product of the set of reactions illustrated above is Prostaglandin H2. It serves as the starting material for building the actual signaling molecules. The followin illustration (from Wikipedia) shows the diversity of possible fates for PGH2:
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Needless to say, there's "a whole bunch" of different molecules here. Each does its own thing, telling different types of cells in different parts of the body to do different types of things. Most of the information available -- and most of the interesting findings -- concern PGE2, in the middle right of the above illustration. The interesting comparison is with PGE3, the analogous molecule produced from the ω-3 fatty acid, instead of the ω-6 fatty acid.
PGE2
PGE2 is an inflammatory mediator. When it is produced, it triggers inflammation. It is commonly produced in response to wounding, but can also be produced in a chronic fashion -- not produced as rapidly, but over a very long time. As with the production of the other prostaglandins, its production is blocked by aspirin and other similar non-steroidal anti-inflammatories. This is how they function.
PGE3
PGE3 behaves differently. Cells that produce it seem not to respond to their own signaling, the way that PGE2-producing cells do. Other cells seem to respond to PGE3 more slowly, and less dramatically. As a result, a diet rich in ω-3 fatty acids causes the production of this form of the signaling molecule, which tends to lessen the degree of inflammation.
Acute inflammation due to injury still produces enough PGE2 to perform the necessary tasks of recovery, but the PGE3 seems like a good candidate for lessening chronic inflammation. If we think of our bodies as responding systems, we might call them "twitchy" when they rely solely, or primarily on PGE2. Adding PGE3 removes the "twitchiness."
The ratio of ω-3 to ω-6 fatty acids
Much is said in the popular literature, and in dietary supplement and natural foods websites, about the ratio of the important unsaturated fatty acids. It is estimated that the "natural" diet (before food-processing and possibly pre-agriculture) gave us far more ω-3's that we now consume. With a similar, or higher quantity of ω-6's in our diets (higher due to food processing, and the replacement of grass with grain for animal feed), the ratio of 3's to 6's has gone way down.
The medical literature has not reported that the ratio is particularly important. It may prove to be after the studies have been done, but so far, the evidence is lacking. More significant is the total quantity of ω-3 fatty acids. This makes sense: the ω-3's are a minority of the total fatty acids in any event, so increasing our intake of these will have a bigger impact on the overall ratio of 3's to 6's than will decreasing the amount of ω-6's. It's pretty easy, for example, to increase a low number (say, 2) by 100% (to another low number, 4). It's much harder to decrease a large number (say, 200) by the same factor (down to 100).
Dietary Strategy
If one intentionally chooses to follow a dieatary strategy that maximizes ω-3 fatty acids, it is likely that that total quantity of ω-6's will decrease on its own without special attention. Grass-fed beef is preferable to feedlot beef for a number of reasons, the fatty acid content being one of the less pressing. It also makes sense to eat a wider variety of fruits and vegetables, rather than eat potatoes as the primary or only vegetable in the diet. The colored compounds (and many of the non-colored ones) in fruits, vegetables, and leafy greens act as antioxidants, and have their own health benefits. Eating whole foods, prepared at home by yourself, rather than eating processed convenience foods, has further benefits. Good meals is one; so is the benefit of getting to know your family again, as you sit around the table and enjoy dinner.