Direct entry of air
Air can get in directly if part of the system goes below atmospheric pressure. This will happen if the following combination of circumstances occurs:

The speed of the pump is sufficient (more speed gives more head)
The flow resistance round the circuit is great enough (more resistance gives more head)
The head provided by the feed/expansion cistern is insufficient (vented system - as used with most conventional boiler installations) or the pressure vessel pressure is insufficient (sealed system - as used in most combi boiler installations.
The pressure reference point (the feed/expansion cistern or pressure vessel connection) is in the wrong place (i.e. near the outlet of the pump, so that the pump subtracts from rather than adds to the pressure).
Air can enter via compression fittings, valve stems or the vent pipe, and it is often very hard to find where this is occurring, because when the pump is switched off, water will not necessarily leak from the entry points. It is therefore a good idea for none of the system to be below atmospheric pressure, and this can be achieved by making sure that not all of the above conditions are satisfied. Moving a feed/expansion connection or a vent arbitrarily is not a good idea, however, because it may pose a safety risk if the boiler overheats, and may lead to pumping over. One advantage of a sealed system is that air entry via the vent pipe and pumping over cannot occur. The pre-charge pressure (normally 1 atmosphere: equivalent to 10m) is also usually greater than the feed/expansion head, although this will slightly increase the risk of leaks.

Air dissolved in water
Fresh water from the mains contains a lot of air, which is why it is not fed through your radiators or conventional boiler, and is one reason why the hot water cylinder has a vent - the air is expelled when the water is heated. (Another advantage of having an isolated body of water in the central heating system is that there will not be much scaling in hard water areas.) After filling a drained system, it can take weeks for all the air to be expelled, because if it is not caught by vents when the water is hot, it may re-dissolve, and most vents don't function effectively with the pump operating, as bubbles are swept past them in the water flow. (Centrifugal and other types of vent which actually have the flow passing through them rather than being teed off, ought to be better in this respect.) Although intuitively it would appear that a radiator would make an ideal air trap, this doesn't seem to happen either!

So apart from not draining the system every other week, leaks should be avoided, as these cause more dissolved air to be introduced as the system is topped up. Leaks are much easier to detect than air entry, but can often go unnoticed if they are in obscure places or are slight. Another advantage of a sealed system is that leaks are not topped up (or not topped up indefinitely), so that not only is the damage caused by a catastrophic leak minimised, but minor leaks will make themselves known by the reading on the pressure gauge dropping. Of course, if regular checks are not made on the system pressure, the leaks will not be noticed until the system is in danger of running dry, which is why sealed system boilers need overheat thermostats.

A small amount of dissolved air will be introduced to a conventional system via the open feed/expansion cistern, if there is enough thermal contraction to draw water all the way from the cistern to the primary circuit when the system cools. Far more air will be dissolved if pumping over occurs - the pump forces water through the vent pipe and into the expansion cistern, becoming thoroughly oxygenated, circulating the already-oxygenated water in the cistern around the system, losing heat and introducing fresh water as clouds of steam are emitted, and for good measure causing mildew or dry rot in the roof timbers as the steam condenses on them. As you can see, pumping over is not A good thing. It is caused by a similar set of circumstances to parts of the system being below atmospheric pressure, but laying out the feed and vent positioned to avoid one problem makes it more susceptible to the other.