First I should point out that "clearing" was an ongoing process and usually pioneers would clear as much as they could to begin planting crops and then add more acreage as the years went by. There were no luxuries like time to wait to get it cleared. Unless you have very large and expensive machinery, the process is the same although mechanization has sped things up considerably.

Typically you would start by clearing out the underbrush. This can be accomplished by fire, using livestock, or just cutting by hand. Once you have that part done, the next step is going to be to fell the trees you want to remove. This was done with a saw/axe and each tree is cut and felled. The next step is to use an axe to remove the small limbs from the trees, if the tree is to be sold or cut up for wood, otherwise it would be piled up and burned.

Let's say you intend to keep the wood for firewood as most pioneers would. So once you have felled the tree and trimmed the limbs you would have to snake it out of the woods and into the open so it could be cut up or loaded onto a trailer for sale. This was originally done with Oxen, Cows, etc work animals. If the tree was too big to be pulled by your animals, you may need to cut it up further before moving it.

Once you have removed the trees, you would have to begin clearing the ground. As early colonists would not have had machinery, they would typically just let the stump rot until it could be pulled out by their animals later or would use a specialized axe to cut up the stump and roots. In the meantime, they would begin to plow the land to break up the soil and avoid the roots/stumps. During this time, they would remove rocks, roots, or anything else that could be an obstruction to planting.

As to the time to do this, that is highly subjective and based on the rockiness or softness of the land, the types of trees and the environment. If the ground is very hard or rocky and in a colder environment, you would not be able to work as quickly. Whereas in the south, you would have been able to work pretty much year round. I can provide an example. My grandfather cleared 80 acres of pine and oak from the South Arkansas delta region in 10 years. Then he spent the next 40 years cleaning up old stumps, rocks, and anything else still in the pasture. He did all of that by himself, with a small personal tractor, bush hog (tractor mower to cut brush) and a chainsaw and that was in the 1940s-1950s. Someone without powered tools alone would only be doing an acre a year most likely, but again this is highly subjective and relies on numerous variables.