Most basic photo editing can be done in Preview, including cropping, resizing, color adjustments, annotation, cut/copy/paste, etc. It's much "lighter" than Photoshop, using far fewer system resources. I rarely need to do anything to a photo that Preview can't handle.
Open the photo you want to extract something from, then either use the Rectangular Selection, Elliptical Selection or Lasso Selection tool available under the SELECT toolbar button.
Make your selection, press CMD+C, open the photo you want to paste into, press CMD+V and move the pasted object where you want it (you can use the ARROWS for finer movements) and after you have finished, press ENTER to "combine" the object with the photo. Then save it however you like.
But know, that Preview does not offer layers, thus you can't remove the pasted object after you pressed ENTER, unless you undo the action.
You can also look at GIMP for a free alternative to PS.