To do a good job of making selections depends a great deal on the particular image. Often, making an outline with the Pen tool set to paths and then turning the path into a selection is a good technique. If the contrast between the subject and background is great, the magnetic lasso tool may be valuable. Then there is Filter > Extract option which works very well but takes a little learning.
Remember to use the zoom tool when you are making selections for a better job.
A good tutorial on the selection tools was written by
theKeeper. Scroll down just a bit on this page...
http://photoshopgurus.com/tutorials_beginner.html
Lots of additional tutes on selections are available on the internet. Just Google 'em.
Once you have the selection made, use Layer > New > Layer via copy Control (Command) J . Once your subject is copied to a new layer you can drag that layer to a new image for a composite.