How do fish get into natural ponds, such as ponds that were formed during the ice age from the melting of glaciers?

One mechanism is that tiny fish eggs attach to the legs of birds that are visiting populated ponds, then come off into the new ponds and hatch there.  Of course, from the point of view of a single egg, the chances of this working a tiny -- but fish lay so many eggs that the chance of getting one or two eggs to a new pond in this way is not bad.

Flooding rivers and ponds will occasionally help fish cover quite a big distance to reach other water sources. As Mike correctly points out, many transfers seem to be with fish eggs or larvae being stuck to water plants or snails that then get taken across land on birds feet.

There might be only a few or even one egg taken a time, but over a few years the hundrerds of ducks, herons, geese and other water birds that will use any small pond every year can easily transport enough animals and plants to start a thriving ecosystem. In fact Charles Darwin did some experiments on this as part of the Origin of Species to show how fish could migrate.

In addition, humans spread fish to increase their chances of future catches. My grandfather told me that when they were dependent on these resources for surviving in Norway, they used to catch trout in the larger lakes in the Norwegian mountains and release them in the larger of the lakes without fish to establish a population. However, this has been going on for many hundreds (or maybe even thousands) of years, and nobody knows which lakes were inhabited by fish introduced by humans and which introduced by birds.

I may be wrong (if so please correct me!) - but I was  under the impression that the "duck feet" mode of transport for fish eggs was a bit of a myth. That is to say it may happen but there's not too much evidence for it.

More generally, its really important to remember that ponds which are now isolated may not always have been and actually would have been connected to each other, and to the sea, in the past. For example, in places like Iceland where glaciers have retreated recently (comparatively.. we're still talking 10000 years), there are many isolated lakes containing fish that would have colonised from the sea (e.g. Arctic charr). As the ice retreated and land rose, the river courses changed and populations would have found themselves in  isolated lakes where they've been ever since.

Also to add to Eric's post. You should never underestimate the impact of humans moving fish. Fishermen have been stocking ponds for as long as they've been catching fish. In the UK there are many non-native species that live in ponds and lakes (e.g. carp, supposedly introduced by the Romans), and in parts of N America fish like the smallmouth bass have been spread far outside their original range because anglers like to catch them.