Half a sphere is a pretty basic model. It sounds to me like you are just having trouble how to figure out the buttons in a given tool. In which case pick something and ask how to use it.
In Wings you right click in a blank scene and choose "Sphere." Now hit X to switch to a side view. Click and drag to select the bottom half (hit Space to unselect if you don't do it right the first time) and then hit Delete.
In Wings you right click in a blank scene and choose "Sphere." Now hit X to switch to a side view. Click and drag to select the bottom half (hit Space to unselect if you don't do it right the first time) and then hit Delete.