Partition walls are generally made of two things: wooden studs (either 2-by-4 or 2-by-6 inch) to create the frame, and drywall (also known as plasterboard) to cover the frame. Removing a partition wall is a fairly simple process that requires a little muscle, though you should be aware of two things. First, make doubly sure that the partition wall is not a load-bearing wall. That is, no weight from the structure of the house is "pressing down" on it, or is reliant on the partition wall in any way to ensure the house's structural integrity. Secondly, removing drywall is a dusty process. Close doors to other rooms, and remove ornaments that can easily be broken. It's also a good idea to put down a plastic sheet to help protect the flooring.
Run a tradesman's knife along the corners between the ceiling and partition wall, and side wall and partition wall, at least three times (do this on each side of the partition wall). This will help the ceiling and side wall drywall stay intact when the partition wall drywall is broken away.
Remove any baseboard that is attached to the partition wall by knocking a small crowbar (or large flat-headed screwdriver) with a hammer down between the top of the baseboard and the drywall. Once the crowbar has been inserted at least an inch, pull it away from the wall. Knock the crowbar down further if required, and pull it away from the wall a second time. Repeat this until the baseboard has come away from the partition wall.
Put on a pair of workman's gloves, and a pair of workman's eye-protecting glasses. Use the hammer to break the drywall close to the top of the partition wall and by the side wall (be careful no to damage the ceiling or side wall drywall). It should break quite easily. Pull away the drywall by hand. Continue in this fashion down the partition wall by the existing wall, knocking with the hammer and then pulling the drywall away by hand.
Remove the rest of the partition wall on one side, then remove the other side of the partition wall the same way. You should now be left with generally bare studs. If the studs have been screwed to each other, start at one end of the partition wall unscrewing the vertical studs from each other. Once removed, place them in a pile at one side. Remove all studs in like fashion, until you are left with a stud attached to the ceiling, floor and side wall.
Remove the remaining studs also by unscrewing them. If the studs have been nailed together, cut each vertical stud roughly in half with a power saw. Pry each stud away from the top ceiling stud and bottom floor stud, by hand. Be careful, as some of the studs may have nails in the end. Knock the end of the crowbar in between the top ceiling stud and ceiling drywall at least an inch (be careful not to damage the ceiling). Pull the crowbar down a little, before knocking the crowbar in a little more. When the stud loosens from the ceiling, move along the stud two feet and carry out the same steps. Do this until the entire ceiling stud has been removed. Complete these same steps with both the wall and floor studs.
As you remove the drywall, you may want to put the broken drywall into heavy duty construction trash bags as you go. This will help decrease the amount of dust in the air, and on the floor. If the studs are screwed together, they may be in good enough shape to use for another project.