There are numerous ways. There are specialised pieces of software that will do this and PaintShopPro has a number of sophisticated screen capturing tools built in but the simplest way is to use the built-in features your probably computer already comes with (this won't capture your cursor or other dynamic features):
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Mac:
command+shift+3 captures the whole screen
command+shif+4 gives a cross hair you can use to select an area of the screen
command+caps lock + shift + 4 + click in a window captures the entire window, neatly trimming out everything else.
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PC:
Print Screen button captures the whole screen.
ALT+Print Screen captures only the active window
On standard keyboards the Print Screen button is usually up on the right-hand side of the top row of buttons, left to 'scroll lock' and right of 'F12'.
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Once you have the screenshot on your clipboard you'll need to open your graphics package of choice:
PaintShopPro and PhotoImpact - you can go to edit and select the paste as new image option (wording may differ).
PhotoShop - open a new graphic (it detects the size of the image on the clipboard and creates a new one the right size) and paste it in.
Many image 'viewers' also have the ability to save images from the clipboard to a file.
Irfanview, Microsoft Paint - hit CTRL+V (the standard shortcut for pasting under Windows) and select "File/Save As".