There's a couple of options here.
1) Paste the screenshot into Paint rather than your document, then use the selection tool to select the area of the screenshot you want, cut (ctrl+x), open a new paint image (File\New), then paste (Ctrl+v). Save this as an image file and them insert into your document.
2) Paste into word, and use the format picture toolbar to crop your screenshot.
Shouldn't be too difficult. I'd go with option 1 though.
PS - I'm not too sure why you are using Alt+PrtSc, PrtSc should do it.
If you don't mind spending money on software I use SnagIt for all snap shots, it works great and I use it for all training type documents.