Gas stations are fairly simple. You simply drive up to the pump, select your fuel, and then fill your tank. You pay afterwards in the shop. I've only seen the pay-at-the-pump option once in all of Germany. Most service stations in heavily trafficked areas remain open 7 days a week.
Other than the signage (learn it!), there's only a few important differences between driving in Germany and the US that you need to know beforehand. The obvious, there's no speed limit on the Autobahn network unless specifically posted. Less obviously, there's implied speed limits for driving in towns or cities and on country roads that may or may not be posted. When you see the name of a town on a sign like this (the Ortschild), it means not only have you entered the given town, but the speed limit is now 50 km/hr. You may not otherwise see a speed limit sign, but there could be a radar camera that traps you just the same. Likewise, the crossed out town name means that you've left the town, and the speed limit now reverts to the rural limit of 100 km/hr.
Next, there's the confusing "priority on the right" rule. Well, not so much confusing as that it goes againts you're US-trained driving instincts. Fortunately, though, it only applies on secondary road intersection where no other sign indicates who must yield. In practice, you only find these in residential neighborhoods and some industrial zones. The rule won't apply for the overwhelming majority of the roads you are likley to use, because priority will be signalled with signs and traffic lights. But basically, it means that at an unsigned intersection, you must yield to traffic on your right, not whoever arrived at the intersection first.
Speaking of priority roads... you'll see this sign on most of the roads you will likely drive on. It signals that you have priority, and other drivers turning onto the road from side streets must yield to you, unless another sign or traffic light indicates otherwise. Hence, "priority on the right" does not apply for you.
Finally, there's no turn on red unless you see this arrow. This situation is not very common, however.
That's a start. As noted, familiarize yourself with the road signs. Most of them are obvious, some aren't. The only German words you should know are "Ausfarht" (exit, specifically for driving, as opposed to "Ausgang" for a pedestrian exit from a building), "Bei Nasse" (means that the indicated restriction applies in wet weather), "Kreuz" or "Dreieck" (cross and triangle, or in this context, an intersection of Autobahns), "Umleitung" (detour, the route is indicated by an orange arrow), "Staugefahr" (roughly, "danger, traffic jam) and "Eindbahnstraße" (one way street).