A better, more accurate (though slightly more complex) method to cut out is to use the 'Alpha Mask Import Plug in'. This method makes the edge pixels transparent (much like feathering does in the above example) which will help it integrate into your new background later. I started to prepare a video tutorial on this method, but never finished it. I'll try and find it - if I can't - I'll make a new one...
Here goes...
1a.Open image you wish to cut out
1b.create a new layer and fill white, change opacity to suit image (white as possible but clarity of 'background' layer is still required)
2.Create new layer (don't forget to name your layers BTW - it is a good habit/practice to get into whilst learning)
3.Ensuring the newest layer selected, select 'Line/Curve tool' (Keyboard Shortcut 'O')
4.Make sure you select black (you can change the layer opacity ~200 to make it transparent, which will make placing this line easier)
5.Select a line width appropriate to your image size (you want a little overlap, the alias of the line WILL BE IMPORTANT)
6.Use multiple, overlapped lines/curves to outline your object, being careful to line the outside of your line with the outside edge of the object (ie the outline of the area you want) - use the 'nubs/handles' to make the curve meet the edge nicely
7.Once finished, ensure you enclose your shape (ie make the ends meet)
8.Use the magic wand to select the transparent area outside your mask, as well as most of the anti-aliased outside edge (try tolerance about 68-70%)
9.Invert the selection and fill the selection black (the black area is your mask)
10. merge the layer down to the white layer below and return both layers' opacity to 100%
11.select the mask layer and copy to clipboard (Ctrl+C)
12.select the background layer (originally opened image) and use the Alpha Mask Import (Effects > Alpha Mask) - delete the mask layer (unless you want it later)
13. Save the image (save as a .PNG file to preserve transparency - if you didn't delete the mask layer, turn it off first)
14.Open the image you want it in and use 'Layers > Import from file' to open the .PNG you just created
Notice how the cutout object merges nicely into the new background with its own pixels, not estimates feathered in... beautiful...