The answer depends a bit upon what you mean by steps, and also upon the specific timber, whether on a farm, or in a forest, that you're referring to. I'll assume you are referring to harvest of naturally grown (as opposed to plantation grown) trees, and that you're willing to consider processing points like lumber mills or paper makers as "black boxes", where an unspecified number of internal steps might take place. The answer also depends upon what time period you're speaking about, as changes in equipment makes the answer today different than it might have been 30 or 60 years ago.
The first transportation step occurs after the tree is felled, and the limbs lopped off to make a log: the log is transported at the site to a place convenient for initial loading. 60 years ago, this step would have involved animals (pulled by a team of horses or mules) or mechanical means (a cable attached to a winch, which pulled the log to the central loading point. Today, it typically involves a piece of heavy equipment called a skidder. (At least in most cases: it turns out that in some cases today, animals are still used, as there are places the animals can go, that the equipment cannot, and there are trees which grow in those places which are valuable enough to be logged, especially hardwoods. More info, use your favorite search engine, and use "horse logging" as a search parameter.)
The second transportation step occurs immediately: the logs brought to the central loading point, are loaded on equipment for further transport. The equipment used in this second step today is most often a truck or tractor-trailer; in historical times it might well have been a logging railroad. Depending upon location, the destination of this step will either be a wood yard or an end use point. Wood yards are found where there is significant amounts of logging, but where end use points have never been built, or where they were built, but became uneconomical to operate. At the wood yard, logs will be kept segregated by species of tree, and will be shipped when ordered for delivery to an end use point. When the destination of the second step is an end user, this transport step today is usually accomplished by tractor-trailer, or by truck.
Also historically, this second step sometimes occurred by water: the wood yard was located on the bank of a river, and when transport was required, the logs would be dumped into the water, assembled into rafts, and guided downstream.
Sometimes wood yards do a bit of preliminary processing, cutting logs to into short wood, which is used in making paper. In other cases, the wood yards ship long logs (40 feet or more). In either case, shortwood or long logs, the items are loaded onto railcars, the type of railcar depending upon the length of the wood, for shipment to a an end user as the third transportation step. Shortwood always goes to a paper mill, while traditionally long logs typically went to a lumber mill, but I understand some paper facilities have been adopted to handle long logs, too.
Where the destination of the third step is a lumber mill, the logs are sawed into lumber. Depending upon the location of the mill, relative to the location of the customers, the lumber will be loaded either onto flat cars, or onto highway trailers for shipment to the lumber yard or, in some cases, the customer. In the case of plywood mills, the sheets of plywood may be loaded onto flat cars, or into box cars. Waste from the lumber and plywood mills is often chipped, and loaded into large capacity open top hoppers or gondolas, and shipped to paper mills.
Where the destination of the third step is a paper mill, the products are shipped out in box cars, or highway trailers in the fourth step.
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