Copy and paste a selection of an image

Everyone else beat me to it

don't copy and paste.

The masking approach is the way to remove things from the image. you than copy that layer on to another job.

Here is why.  copy and paste or erase are very destructive actions as in there is to way for you to edit things if you need to make changes or make a mistake. The key to photoshop is to find a way to do things so everything is editable.

Learn mask or you will be pulling your hair later because you need to redo things over and over when needing to edit things.

You need to learn selections and masking. There are many ways to make a selection and cut out part of an image. You have all of the selection tools, the pen tool, quick mask mode, select and mask, etc. It really depends on the image and what you are trying to cut out.

I would place both images in a single file, make your selection the best way you can and use a layer mask to hide the rest of your image.

Photoshop Selections, Masks & Channels - YouTube

The method you choose for cut-outs depends on the  type of image and your skills.

Quick and dirty (to get the idea) use the lasso tool to select a bit of the pic. Cmd/Control + J to put the selection on its own layer.

In the latest version of Photoshop you can copy and paste that layer onto another image (Layer).

There are lots of ways, and you should use non-destructive methods (not what I suggested above!).

I suggest you have a look at the online video tutorials on Lynda.com. (You can get 30 days free)