Conceptually it's not that difficult. Signals that are modulated and sent over the air are picked up by the antenna and fed into a computer that conducts the same signal processing (via software) that a normal radio does (either via software and DSP, or by good old fashioned LRC circuits and oscillator).
If you're still in Alaska, you should go to a MARA meeting. http://kl7jfu.com/ If you actually want to learn about radio (learning Amateur Radio WILL help you make your military comms much more effective, IMHO) just PM me and I'll give you a dude to link up with. He will show you more about radio than I will ever know. He operates the club repeater at his house, also was a FF/medic in Wasilla.
As to the SDR dongle... I don't do much RX only work at all. What I do do, I do with my handheld or my mobile units. Even the FT-857 will interface with windows, android.... ehh, I haven't tinkered yet with that and honestly the furthest extent I would possibly be going is a USB to DB9 adapter to do packet with a terminal on my tablet. If you're just trying to pick up AP.25 stuff for local SA, I still think you'd be better off with a standalone scanner due to being able to input the audio to anything, and a form factor that allows more portability without requiring you to fire up a computer.... Looks neat though.
So thats Balint, he works for a company called Ettus Research.
Here is a pic of me and him from the last Defcon in Las Vegas (so you can tell I know what I am talking about).
You asked if anyone had experience with SDR dongles:
This is my personal collection of publicly available SDRs. Starting from the top left going clockwise that is a HackRF, a Ettus B210, a Nuand bladeRF, a E4000 based tuner, a Nooelec TCXO R820t, a Funcube pro, a Ubertooth, a Nooelec R820t2. The Dongle at the bottom is a hybrid E4000/RTL2832 with the new antennas they ship with.
Depending on what you want to do the RTLs are great for amateur/backup use. I normally carry a few around with me where ever I go, the packaging looks like this:
This particular dongle runs $25. Cheap enough to throw away or leave behind if need be.
If you have any questions about how they are useful, the differences between models, or how to get started with them I am happy to help.
One quick example of what they can be used for is creating a heatmap over time. Using the free tools rtl-power you can create a map of the visible spectrum in the devices range that looks something like this (a 24 hour example):
If you combine the rtl with a low priced platform like a beaglebone or raspberry pi you can build an effective spectrum monitoring tool for less than $100. At that point there are a ton of fun things you can do like attach a battery, add a cellular modem and mail the package to someone.
Believe me I have the same exact problem. Ettus recently released the E310. Its basically a B210 thats smaller and in a rugged case. Here is mine with some gear I was reverse engineering. The bladeRF on the right provides a size comparison.