
This is the image we are going to work with. As you can see, it has an annoying white halo around it, which makes it less than perfect. What's a halo, you ask? The white pixels surrounding the image, that's what it is. Of course, halo might be any other color. Halo makes an image look unprofessional and that's why we have to find a way to eliminate it.

First use your lasso tool,

and select "point to point" as the selection type. Confused with where the tool options might be? Then right click a grey spot in the program window and enable "Tool Options" from the drop-down menu that will appear.
View screenshot.

It's better to zoom in the image, so that you can be more accurate. Then, using the lasso tool, select the area you want to have clean edges. That's quite difficult. Remember that the more points you have the better your selection will be. Press the left mouse button to join up each point and right click when you are finished. You may need to modify your selection by pressing shift to add to the selection or control to remove from it. Try to leave out as many black pixels as possible. In order to make selections quickly of course, you need training. Don't expect your first selections to be perfect!

After you've finished your selection, go to
"Selections >Modify >Contract". You should set 4 as the number of pixels. Then go to
"Selections >Modify >Feather" and set 2 as the number of pixels.
That's it! Now you are ready to copy the selection and paste it wherever you wish. If you like, you can paste it to a lighter background(for example, bright green) to remove any black pixels that may still be there. To do that, either use the lasso tool to select them and then clear the selections, or use the eraser brush to rub them out. If the result is not what you expected, you should try and remove more things from the selection, contract and feather it more or less. Play around with the values and you should get it done.
Example