Photoshop 7.0

Hold down the shift button and use the magic wand tool until you have your entire selection area mapped out. Then delete or cut the selected area.

You should be able to copy and paste like you would in any program. Open the picture to be inserted. Then Ctrl + A to select the whole. Ctrl + C to copy to clipboard. Then open the picture recieving the other graphic and Ctrl + V to paste what you copied.

When you do this the pasted image will be on a new layer automatically.

There are many selections tools you can use. You can select by color, color range, marquee etc.

In the end, however, the best results are going to be achieved the tedious way.

When I do this, I make a duplicate of the source, then use the polygonal lasso at a very high zoom level. After I've made my selection, I go around with 1 to 3 pixel eraser and get any stray pixels.

Good luck.

I simply zoom in about 300% and use the eraser tool around the subject. Like dM said, you need it on it's own layer and not the background layer though.

you can use paths aswell if you are fluent with them, that way you can use them for a mask in illustrator too

*hopes he's not too late*

Use extract!

That thing rocks, opens up a window and you draw round the images, then fill in the bit to keep and hit ok, and it's almost perfect!

Filter/extract

Just to firm up what ATNO suggested, you can use the magic wand as a much quicker way to go through and select the certain colors. If you are combining two images this can be helpful if the back grounds or colors are close to being the same. If your combing two older photos that are grainy, it can be hard to be real exact and having the speed of the magic wand is a nice trade off.

As an example, my wonderful mother (who isn't a day over 55 ) wanted two old photos combined. One was of her grandmother and the other was of her grandfather and grandmother that had gotten a watermark on it. I tried being precise, but it wasn't going very well because of the photos being in only black and white it was hard to follow exact edges. So, I used the magic wand, and in 15 minutes I had a brand new photo printed, framed, and in a box for my mom. Badaboom Badabang!

I find using the 'MagicWand' to be easier to use when trying to get rid of the background.

colour range works very much the same way too.

Exactly what I do, I find it easiest because if you screw up just undo the one part rather then having to re lasso the whole thing.

Extract is a great way to do it, also great for cutting around images which have things like hair etc.