Hopefully you've read the article on how to figure out how much materials you will need to purchase, before building the wall. Once you have figured out and purchased your building materials, it's time to learn how to assemble the wall.
The first thing that were going to want to do, is fasten our bottom and top plates, to the floor and ceiling. Let's start with the bottom plate. Measure the distance in between the walls, where you are going to be installing your new wall, and cut your bottom plate to fit in that area.
Place the bottom plate, in the area where you are ready to frame the new wall and then measure the distance from each end of the wall, to the other wall that runs parallel with your new wall. Make sure that these distances are even at each end and even in the middle of the new wall that you are about to frame, before attaching your floor framing plate.
Then you can fasten the new wall bottom plate to the floor. This can be done with nails, if you're building on top of a wood framed floor or you can use shots and pins, to fasten the bottom plate to a concrete floor.
After you have fasten the bottom plate securely to the floor, you will need to use a building level, to mark the vertical placement of the end of wall studs, that will be fastened to each side of your new wall.
After this is done, you can install your top plate of the wall, and make sure that it runs in the same direction as the bottom plate. This can usually be done by using nails, but if you don't have anything to nail to, there's a good chance that your going to need to open up the drywall ceiling, and install some wood blocks that will provide your new wall with a solid surface to attach your new framing top plate to.
After you have secured your bottom and top plates, you're going to need to grab your tape measure and start at one side of the wall and mark your bottom and top plates, 16 inches on center and this will be where you're placing your new vertical studs.
After you have laid out your bottom and top plate, it's time to measure the distance for the new vertical studs that will be installed. Always start at one end and work your way towards the other end.
Simply fasten each vertical stud, driving two nails through your vertical stud, at the bottom and top plates. This method is often referred to as toe nailing and is the method that I would recommend, for building your new wall.
By now, you should be looking at a nice new wall that you have framed, or you have been completely frustrated and need more information. I hope this information helps someone.