The thing to determine first is, is it the printer's fault, the computer's fault, or the software's fault? To check whether the printer is at fault, try running the printer's self-test (check the printer documentation for instructions on how to do this). I don't care if you just did a self-test last week, do it again! If the printer can't print by itself, check the ink/toner level, paper jams, etc.
Once the printer alone is working, run a simple test through the computer (NOTE: this may not work with plotters or PostScript printers): from the DOS prompt, type
COPY CON: LPT1: This is a test. 0123456789 ABCDEFGHIJKLMNOPQRSTUVWXYZ
After entering that last line, hold down the Ctrl key while typing LZ, then press Enter again. The computer should respond with 1 file(s) copied and the printer should print out the test line. If something different happens, there is a problem in the connection between the computer and the printer. Make sure the printer cable is plugged in properly, or try a different cable if you have one.
If everything is ok up to this point, it's time to check your software. If it's a DOS program that has trouble printing, you're on your own. For Windows programs, the first thing to check is whether you have the proper printer driver installed. Open the Control Panel, go into the Printers section, and make sure the Default Printer matches the actual printer you have.
Most printers these days include a set of disks that you need to install to make the printer work with Windows. Be sure to follow the instruction manual precisely on how to install the drivers. If you run into problems during this step, contact your printer's manufacturer for help. For users of Windows 95, Microsoft has provided the drivers for you; simply double-click on Add Printer from the Printers folder and follow the directions on the screen. If your printer manufacturer didn't provide driver disks and Windows doesn't come with your exact model listed, check your printer manual for a compatible driver that Windows does come with.
The next thing to check is what Windows thinks the status of the printer is. Open the Print Manager (in the Main group) and look at the Status column for your printer. Normally the status should be "Idle" when the printer is not in use, and there should be no documents waiting underneath it. If the status is "Paused", simple press the Resume button.
If you are getting unexplained error messages while printing or parts of the printed page are missing, you may have a memory problem or software conflict. How much space is free on the hard drive? Check the File Manager to find out; you should have at least 5-10MB of disk space free for temporary printer files. Also, since the video driver has a say in printing too, try using a generic video driver such as Super VGA or VGA. Run Windows Setup to change this.