To do transparency, do the following
Click on Layer > Transparency > Add Alpha Channel
Then select the area you want to make transparent, either with the square or select by color, etc...
Once highlighted, press Ctrl-X to cut that area, and it should leave a transparent space in the image.
Once done, save as a gif, because jpg doesnt support transparency.
To copy from one image to another, select the space to copy (or the entire image), and press Ctrl-C.
Switch to the other image, and press Ctrl-V.
To resize an image, right-click on the image and click Image > Scale Image.
Select the pixels you want, and click Scale.
To crop a picture, select the area you want to crop around, and right-click, then click on Image > Crop Image.
A combination of all these is how I made my Apple-BSD logo on the left.