I don't use Coffee Cup myself (I prefer Animation Shop, seeing as its easier to get my sprites from PSP and just import them) but here's how I think its done
Require materials: Paint, Coffee Cup
Firstly: In Paint, get your sprites and put them in the position you want for the first frame. Also make the dimensions (Options, Attributes) in pixel format, around 250 by 200 is what I use
Secondly: Select All (Crtl + A) and then copy (Crtl + C)
Thirdly: Open Coffee Cup, make a new animation and set the dimensions to 250 by 200 pixels
Forthly: Paste in what you've made into the first frame. Then, right click somewhere on the window or check the various menus until you get an option called "New Frame", which you should then make one of
Fifthly: Make the next frame in Paint, paste into the second frame in Coffee
Sixthly: Repeat the process
Seventhly: When done, save in "My Pictures" under any filename
Eightly: Upload to the net via an image hosting site, like Photobucket or Imageshack
Tada, animation on the web