Do I assume that your small 200x200 image has a white background?
If so, you're gonna have some problems.
What colour background does your main image have? Is it a single colour or is it a complicaed background? What about the background colour of the small image? What is that like?
The first thing you will need to do with the small image (assuming it has a background colour) is remove it's background colour. Then you will be able to paste it into the main image and move it anywhere you want without that horrid little white box.
I'll assume that the small image has a white background.
Open both images. Well work on the small one first.
You may have menus at the top but if not you should be able to get them with a right click of your mouse.
First click (select->by color) and then click on the background. You'll see that the background becomes selected. You might also find that other bits have becomes selected that you don't want to loose like tux's middle.
Now click on the "quick mask" button. You should find it at the left end of the horizontal scroll bar. Hopefully, you have a red mask all over tux now.
If there are bits of tux that are not red (like his eyes and front) then you'll need to paint them back in. To do this, select the brush and just paint over these areas being careful not to go over the edge anywhere onto the white background.
Now you can click on the quickmask button again and you should see the background selected around tux.
Now try clicking (edit->cut) and see if the background disappears. If it does, it will be replaced by a two tone grey checkerboard pattern. This is how Gimp represents a transparent area.
Now you need to look at the edges all around tux to see if there is any white still showing. If there isn't (or it's little enough that you don't mind), you can click (edit->copy) and then switch to the main image and click (edit->paste).
If you do still have a white edge you can use the eraser tool to trim the last few areas. You might want to select a fuzzy brush too to avoid harsh edges.
Finally you can copy it and paste it onto the other image as I suggested earlier.
Hopefully this is enough for you to get what you want.
Let us know how you get on.
Trojan.
Trojan.