The graptolites are now classed as hemichordates (phylum Hemichordata), a primitive group that probably shares a common ancestry with the vertebrates.
In life, many graptolites appear to have been planktonic, drifting freely on the surface of ancient seas or attached to floating seaweed by means of a slender thread. Some forms of graptolite lived attached to the sea-floor by a root-like base. Graptolite fossils are often found in shales and slates. The deceased planktonic graptolites would sink down to and settle on the seafloor, eventually becoming entombed in the sediment and are thus well preserved.
Graptolite fossils are found flattened along the bedding plane of the rocks in which they occur. They vary in shape, but are most commonly dendritic or branching (such as Dictoyonema), saw-blade like, or "tuning fork" shaped, such as Didymograptus murchisoni.
An excellent resource on graptolites is Old as the Hills. You can find them at: