Can someone explain inertial frames to me? How did the idea come about and how is it tested?

Sorry, can't help. My browser doesn't support inertial frames.

A frame is a frame of reference, a way of coordinatizing space and time. One common frame is the lat/lon grid that rotates and revolves with the earth--no matter where the earth is in its orbit, a city stays at the same latitude and longitude. That would be an example of a non-inertial frame.

An inertial frame is one in which the laws of Newton are valid. They are not valid in the lat/lon grid (or other non-inertial reference frames) because "fictitious" forces like coriolis and centrifugal arise.

What interests me is the subject of time dilation and how inertial frames come into play. (This might be a topic worth touching on in a podcast.) For example, we have two people at rest and then person B accelerates away from person A. Seems to me that from each of their perspectives the other should be running in slow motion time. Correct? At some point person B stops and accelerates back towards person A. My understanding is that A will be much older than B, but why? If there is no absolute reference then from B could consider himself to be stationary and from his perspective A may be moving away from him.

I know that there are reasons for the accepted conclusions but I don't have a good handle on them.

Try these:
Twins Paradox
Twins Paradox GR
Twins Paradox Redux

This gives me a headache. Well actually the neurons dealing with these concepts don't seem to be connecting properly.

I'm going to attack this in small chunks.

If Jim and Jan were twins and Jim accelerated away from Jan in a space ship, at this point each one would see the other as moving in slow motion, right?