The chambered part of the ammonite shell is called a phragmocone. It contains a series of progressively larger chambers, called camerae — the singular is camera — that are divided by thin walls called septa —the singular is septum. You can see the interior of an ammonite with the discreet chambers in this lovely sliced Cleoniceras sp. from Madagascar.
Only the last and largest chamber, the body chamber, was occupied by the living animal at any given moment. As it grew, it added newer and larger chambers to the open end of the coil. Where the outer whorl of an ammonite shell largely covers the preceding whorls, the specimen is said to be involute. Anahoplites is a good example of this. Where it does not cover those preceding, the specimen is said to be evolute, something we see in the ammonite Dactylioceras.
A thin living tube called a siphuncle passed through the septa, extending from the ammonite's body into the empty shell chambers. Through a hyperosmotic active transport process, the ammonite emptied the water out of these shell chambers. This enabled it to control the buoyancy of the shell and thereby rise or descend in the water column.
A primary difference between ammonites and nautiloids is the siphuncle of ammonites — excepting Clymeniina — which runs along the ventral periphery of the septa and camerae — the inner surface of the outer axis of the shell — while the siphuncle of nautiloids runs more or less through the centre of the septa and camerae.
Clymenia has a closely coiled evolute shell that may be faintly ribbed. The dorsum, on the inside of the whorl, is slightly impressed, a result of the outermost whorl slightly enveloping the previous. The venter may be rounded or acute. The suture is simple, with a broad ventral saddle, broad lateral lobe, a dorsolateral saddle, and a moderately deep hidden dorsal lobe. Septal necks are usually short and do not form a continuous tube. The suture and siphuncle are characteristic of the family found in Europe and Western Australia.
If you fancy a read, check out the Treatise on Invertebrate Paleontology, Part L Ammonoidea; Geological Society of America and Univ of Kansas Press, 1964.