Technically, the electronics and optics are fairly easy to implement; basically the same kind of setup as the reader in a rotary encoder (an LED focused on the surface to be scanned, reflecting to a phototransistor). Unless you are looking to get into a "contactless" (that is, held a certain distance from the barcode) reader - then the optics can become more complex to implement. I would start with a contact scanner (ie, one that requires the barcode to be within say a few mm of the LED/sensor pair).
Now this setup, when you run it past (or run past it) the barcode, will generate a series of high/low pulses, the width of each determine the value of that point in the code. IIRC, there's also checksum and other values to help you know what direction the barcode was scanned (so you can reverse it if necessary). You basically have to record these pulses, analyse them, then decode them (reversing them if needed), and verifying them using the checksum (if implemented for the barcode type - there are several different standards available) - then outputting the data to your display.
All of this would be best accomplished using a microcontroller; for the code/algorithms needed, google is your uncle (look up "barcode decoding algorithm" and the like - tons of stuff out there to work from).