MarkD already gave a realreally good by the book answer, but let me answer from the side of a homeowner who has had septic tanks for around the last 20 years.
The only time I had any maintenance/inspection was one time when my yard was getting really swampy. I had a septic guy come out and he pumped it rather cheaply, no permanent damage, no big whoop. Those Rid-X commercials with the bathroom full of backed up waste seem like an exaggeration to me.
We try to go easy on the chemicals, but we aren't that diligent about it. Definitely no drain cleaners, but chlorox goes in the toilets regularly.
One thing we do about 2-3 times a year is flush either some baker's yeast. It is effectively the same thing as Rid-X and much cheaper. I've also heard flushing raw hamburger (small quantities) is another way to get the bacteria going, but I'm a little nervous about that idea. I figure my septic tank gets enough hamburger the "regular" way if you know what I mean.