First of all, the resolution of most computer screens is too low to render a readable barcode if the standard barcode dimensions are used. The width of the smallest bar or space in a normal sized barcode is on the order of 13 mils wide yet the screen resolution of most computer monitors is typically 72 dots per inch or 13.88 mils per pixel. Since a computer screen draws graphics using fixed size pixels, it cannot draw bars that have a width that is not an exact multiple of the width of a single pixel. In order to display readable barcodes on a computer screen, you must choose a bar width for your barcodes that is an integer multiple of the width of a screen pixel. For example, if your screen resolution is 72 DPI, then you should use barcodes that have a narrow bar width of 13.88 mils, 27.77 mils or 41.66 mils, etc. This will cause your barcodes to be larger than a normal barcode however they will at least be readable. Also, if the barcode symbology that you want to use supports a "Narrow to Wide Bar Width Ratio", then this value should be set to an integer value of either two or three; with three being the preferred value.
Secondly, there are several different types of barcode readers on the market including wands, laser scanners, CCD readers and camera based readers. The only types that can successfully read a barcode off a computer screen are CCD readers and camera based readers. CCD readers typically have difficulty reading barcodes off a normal glass tube computer monitor however they can easily read barcodes off an Active matrix or other flat panel display. The best type of reader to use when reading barcodes from a normal computer monitor is a camera based reader. The camera type readers actually take a picture of the barcode and use digital image processing techniques to decode the barcode so that it is much easier for it to read off a computer screen. The only drawback to camera type readers is that they are extremely expensive with a typical price tag of $1500 and up.
All other types of barcode readers (pens and laser scanners) measure the intensity of reflected light and therefore cannot be used to read from a monitor because the glass or plastic in the monitor screen does not reflect light back to the reader.