Getting from platform to platform

Depending on the layout of the station you indeed use overpasses or underpasses. Of course it's always possible your connecting train could be on the opposite platform; just a few feet away.

http://www.youtube.com/watch?v=moLGxdId9uU

A little of everything. There are two types of stations -- trains beginning and ending and trains passing through. For station beginning and ending think of fingers on your hands, walk down one platform and over to the other. Sometimes it can be a long walk. Termini in Rome has 25 or more platforms or tracks. Some stations the platforms will be on different levels. The Antwerp station is three levels and several in Paris are two levels.

For stations, generally small one, where the trains are passing through you will find over and under passes. It just depends on the layout of the station.

Many different layouts. Some stations have overpasses, some stations have a tunnel connecting the platforms (probably more common than overpasses). In addition to this, some stations have elevators from platform level to overpass/underpass level, but many do not. At dead end terminuses, you switch platforms at the end of the tracks. Many main stations in larger cities are dead end terminuses, e.g. all major Paris stations are, Munich Hbf is, Roma Termini is. At smaller stations on secondary lines, you often just cross the tracks at a designated pedestrian crossing point. This crossing point can be guarded (with a light and/or a bell when trains are passing) or unguarded (you have to look out yourself). The different European railways have different rules as when to allow pedestrian track crossings depending on the line speed. Here in Denmark it is allowed up to a line speed of 140 km/h if the crossing has warning lights/sound.

In most small stations you take a flight of stairs down to a tunnel that runs perpendicular to the tracks, each stairway is labeled with the platform number - so take the right stairway up and look for the your train.

The big stations also have stairs down and tunnels. In addition to those they have stairs/escalators up to a common area with cafes, retail, etc. where you can pick up lunch or a beer.

And in some small stations you just walk across the tracks to get to the next platform (e.g. Szeged, Hungary and some stations in Ukraine, etc.)

Walking across the tracks isn't very common in western Europe. Most all inter-city main line train stations have platforms; the passenger cars aren't even equipped with stairs that would allow you to exit at ground level. The exception would be narrow gauge train lines found in places like Switzerland. At these stations you indeed walk across the tracks.

thanks for all the input

Reason I was asking, on our Paris to Fuessen ride, we have a very short time at one of our transfers of about 10 minutes in Augsburg and I want to get prepared for what we can expect.

Ten minutes should be ample time. We have had 4 minute conntections several times at different locations and always made it with time to spare. You can usually ask the conductor when he/she takes your ticket which track your connecting train leaves from. I was concerned about the short time too, but it has always been fine.

10 minutes is enough time, and even if it wasn't, you probably wouldn't have to wait that long to catch the next train in the same direction.