Alright, here is the rundown on how the system works in germany (and austria too, though with different players) with multiple parties.
Basically, you have 2 rather large-ish parties (30% give or take most of the time), one that is more right-leaning (actually, its centrist from a US perspective) and one more left-leaning (which is pretty damn liberal by US standards, again), and added to that you have several smaller parties. Now, two of them are important enough (one strictly liberal, and another one being a "green" party) but they arent actually gunning for governing, they are primarily a way for voters to express concern and support for their narrow set of ideas and concepts.
Since there is no serious outer right-wing party in germany, and since the communist party is not really a serious player outside eastern germany, we ll leave that aside.
Now, come election time, there has not been a single party in power all on their own in a long time now, due to the fact that the green and liberal parties usually get between 6 and up to 13 percent, thus making them important for coalitions.
Angela Merkel is from the CDU, which is , for german terms, the conservative party. The problem for them has always been the lack for a good coalition partner. Nobody would ever dream of teaming up with any of the tiny extreme-rightwing parties, and lately these dont even get any seats anymore anyway, so the conservative party needs allies from the left of their position. The lefty-liberal big party, the SPD, has been in bed with the green party (at 9-12 percent a rather big player, too) for a long time now, whereas the leftover liberal party, a party more or less known to be the epitome of opportunistic and shapeless, running only on a small subset of ideas all the time, is not big enough to push a coalition with them over the threshold of being able to push issues through congress/senate equivalents.
The thing is, people do not strictly vote party line here at all. It is possible and actually quite common that a policy brought up by the governing party gains support of a smattering of votes from the "other side", so to speak, and gets passed without trouble even if some of their own guys vote against it. Due to the nature of our multiple parties, it is also quite common that the smaller coalition partners not only get a few bones thrown their way (cabinet positions etc.) but get a say in a subset of policies as well.
So, if Angela Merkel intends to, for example, set a policy about reducing exhaust fumes by the industry, but intends to pay that with taxpayer money, thus making it an unpopular solution with the SPD ( a social/worker party for the most part), it may still gain traction with THEIR coalition partner, the green party, since it pretty much falls into their category of interests, and they would vote in favor of it.
In the end, this usually means that as a voter, I can vote for any party I can see doing a good job, because the resulting policies are usually colored and heavily influenced by all parties, varying with their relative success, rather than having to decide for one party which gets to push through ALL their plans their way.
I hope this made sense.
Austria is a slightly different beast, as it is, for european standards, extremely right-wing. Fully 30% of the population has voted extreme right this last election if I remember correctly, with a populist republican-style rightwing-nutjob party gaining a lot of traction through tactics directly borrowed from the playbook of the recent USA elections. Either way, Austria is a small country which is mainly concerned with itself, and it shows in politics... for a long time now, the two big parties have been in a coalition that gets them absolute majority, but internal squabbles prevented much from happening at all. The only reason they are now forced to acknowledge they did a shit job is that numerous smaller parties, among them the aforementioned rightwing nutjobs and also a green and a communist party have gained a lot of votes, whereas the big two have lost them. Austria has a history of wildly varying election results, a decade ago the nutjobs (back then under a different name, but mostly same personnel) had 4 years of government after a surprising landslide victory, but as most of these european "issue" parties, they dont do a good job actually running the entire thing, so they lost a lot of voters afterwards.
In the end, the one big advantage the USA has in your party system is that you really dont have to give much thought to voting for the most part, as there is just one party for each side of the political spectrum. Also, there cannot be any surprise upsets (as happened in Austria) which catapults a crappy but charming guy to the top who runs the country into the ground within a few years..... oh wait, didnt that just happen a couple years back?
I really like the fact that every election, I have to think and decide who I vote for, and I get the impression that it really matters whether, for example, the green party got 8 oder 12 percent, and not just who won overall.