Industry Specialization in Cities: Skylines

Ok, I just figured this out.

So you see the 'Districts' menu at the bottom of the screen? It's next to the 'Zoning' button.

When you click on it, a number of options will appear above it, the first one allows you to 'paint' a plain-jane district, with the second being 'Erase District' and the remaining ones are for specializations. If you've unlocked the other specializations, all you need to do is to click the one you want, say 'Agriculture', and then click on an existing district or paint a new one.

Districts can be used for a couple of different purposes. Probably the most important trait you can set is the "no heavy traffic" policy. This can be extremely useful if, eg, you create a residential district which would be technically faster to use to go between your industrial and commercial sectors, but you want to have your trucks use the longer freeway that is better equipped to handle traffic and won't complain about the noise. You can also use this to create "no truck left turn" intersections by creating a small district on the left side that doesn't allow heavy traffic.

Other than that, there are more ways to use district specialization. JMR mentioned that you can use the lower electricity or water reduction policies in specialized industry districts (electric can be a net positive in office and high commercial areas as well if I recall). Generally, you'll probably just want to use Parks and Rec and recycling as general city policies, but if you really are pinching pennies you can restrict those to certain districts as well. People will require better land value in high tax areas and won't care as much in low tax areas, I probably don't need to explain why that's useful to set by district.

Another important (if callous) thing you'll need to do later on, once you have a well-educated population, is to create low tax, high density residential areas with no access to education past elementary school so you keep a supply of poorly educated citizens to man your industrial areas. In those areas using the education boost policy is obviously not wanted.

Should you combine different zone types (residential, commerce, industry) into a common district or is there a benefit of keeping different zones in different districts?

This is situational - in general, it probably won't make much of a difference if you combine different zoning types into the same district since most policies are separated by zoning type anyway (taxes, business investment/High Tech Housing), but if you want to optimize the reduced usage policies you should keep them separate (that said, once you get past 20000 people or so money becomes a non-issue).