If I purchase a SIM card for Germany, and I wander over to Salzburg, for example, would I be roaming? How is roaming defined and how does it work?
Roaming is: when you are connected to any network other than your original network. This usually happens when you are in an area where the home network is not available. It can be national roaming (India for example) or international roaming.
The moment you are connected to a network other than home network your roaming charges will apply. So in Salzburg you will be roaming if you are using a German sim card. This is easily identified by the network name in your mobile's screen.
Roaming charges are extremely high in most cases, but in the recent years with the expanding of the telecommunication companies and with a lot of bilateral agreements between major international operators (eg. Vodafone), prices started to get lower. Always check the roaming prices in the destination country before using the roaming service, one country can have multiple operators and the offered nice prices usually apply to one operator. So always check this in advance and set the phone's network selection to manual selection and select the operator with the best roaming prices.
Also, usually international operators (eg. Vodafone in EU, Zain in middle east) will have very low or no fees at all for roaming if your roaming within one of the operator's friend networks abroad.
Wikipedia has all the gory details. Basically, in Europe, licenses for mobile phone operators are issued by each country and networks in different countries are generally separate even if they are operated by subsidiaries of the same parent company or share the same brand (I write “generally” because I am not entirely sure that it's always the case but it's been my experience; In theory, I guess a carrier could cover several countries with the same network or several carriers could strike a deal to let each other's roaming customers use both networks without extra charges).
In the European Union, the Commission has been pushing for lower prices for quite some time and there is a price cap for roaming charges (but between EU-based carriers, I don't know if those rule apply to customer coming from outside the EU). I also heard about some projects to remove them entirely, at least between some countries, but I don't know their exact status. Note that you will usually receive a SMS informing you of the roaming charges as soon as you connect to another network (again, this is my experience using a phone from an EU-based carrier in another EU country, not sure if all of this applies if your home network is somewhere else in the world).
As of 2017, while you may be roaming, (EU) operators will no longer be able to charge additional roaming charges within the EU, per EU law.