A short wall can help end territorial arguments in the children's bedroom, and it can make a large living room more useful by dividing it into sections. It's typically about half as high as a full wall, and because it doesn't attach to the ceiling, it needs more secure anchoring to the floor than a full one. Longer walls need the most anchoring, and there is more than one way to do it.
Erecting a Short Half Wall
Constructing a short wall is identical to constructing a full one. You cut the top and bottom plates of the wall to the lengths you need from two-by-fours, then cut enough studs to space them 16 inches apart with one at either end, and nail them between the plates. Erecting a wall that's less than about four feet is a matter of positioning it next to a stud in an existing wall and driving 3-inch screws into the end stud and bottom plate to hold the wall to the adjoining wall and to the floor.
Setting a Post
The end of a wall longer than about four feet is likely to wobble if you simply screw the bottom plate to the floor and don't make efforts to brace the end stud. One solution is to replace the stud on the end of the wall with a four-by-four. To make this work, you have to extend the post through the subfloor and bolt it to blocking attached to the floor joists with 2 1/2-inch bolts. Once the post is secure, you build the wall, attach it to the post and anchor the wall to the floor and the adjoining wall in the usual way.
Anchoring with Plywood
A short wall at the top of a staircase has to be stronger than one in the middle of the room, because it's there to prevent people from falling down the stairs. A common way to anchor such walls is to cover one face with 1/2-inch plywood, extend the plywood down below the subfloor and screw it to a floor joist. Use 2-inch screws, which are long enough to almost penetrate the joists, and space them about 12 inches apart. You can install drywall right over the plywood once the wall is secure.
A Hardware Solution
If you have access to the underside of the floor, you can securely anchor a short wall without removing the subfloor by using threaded rod and some hardware called tension tie connectors. You first need to nail blocking to the joists, then erect the wall with a double stud forming its end and screw it to the floor. You bolt one tie to the blocking and one to the end stud on the inside of the wall. Drill a hole through the floor, pass a length of threaded rod through the hole and through both ties, then secure it at both ends with a nut. Tightening the top nut puts tension on the rod and makes the front of the wall solid.