If you have a rental car from outside Germany, without a so called "Umwelt-plakette" or environmental sticker what do I have to do to enter the environmental zones? Can I get a waiver if I show that I have a rental agreement?
As you probably know, cars registered abroad are not generally exempt from the environmental sticker requirement. The official websites from many cities are very explicit about that and the law includes provisions to determine in which category cars registered abroad fall. It would therefore be somewhat surprising if rental cars were exempted (after all, promoting tourism and the practical difficulties involved were not enough to justify an exemption…).
The law does however include a provision for the federal government to exempt some vehicles. Those include things like cars used by someone with a disability, official vehicles from the police, etc. but not rental cars (either local or foreign).
Furthermore, the cities and provinces can add some rules. There are many such rules and some of them are especially relevant for tourists (e.g. vehicles with a yellow sticker registered abroad can sometimes be used in places where German-registered vehicles need a green one) but I am not aware of any blanket exemption for rentals. You can find detailed information on these exceptions on each city's website or on the ADAC website.
Incidentally, the police can fine you even if you are not in the car. Since it's increasingly common for fines to be sent abroad within the EU, it would be likely to end up at your rental shop, which would presumably promptly charge you for it. Even if you would actually qualify for some exception, it would seem quite difficult to get the money back in these conditions.
No you cannot get a waiver. Entering the environmental zones without a sticker will get you fined. You can get a sticker for 5 EUR at a TÜV or DEKRA branch by showing the vehicle's registration papers.
while the answers by Michael Borgwardt and Relaxed are both correct, you shouldn't worry about this too much - getting fined just for not having this sticker is not very common. Usually you'd be fined if you get stopped e.g. for driving too fast or parking violations and the police notices the missing sticker. also the police in Germany might be OK if you just tell them you didn't know
YMMV, the whole thing depends a bit on the city you want to visit - in Berlin for example this is handled very relaxed.