If you're a hobbiest who is printing for fun—or if you have a printer without a heated bed—you'll want to use PLA. ABS is tougher but it requires more heat to melt, so it works best with printers that have heated beds (which are fancier and more expensive).
Also, be sure to use the appropriate-diameter filament for your printer: The heating element and melting chamber are generally designed for filament of a specific thickness.
Learn the software
3D printing software tells the physical printer how to move to print a specific object. The software tells the printer things like how fast to push the filament through the extruder, what temperature to heat the filament to, how fast to print the layers, and how the thick to make them.
Some 3D printers don't ship with the necessary software for running them. If you find that the software is missing, you'll have to check the printer manufacturers' website for recommendations or download links.
Some printer manufacturers use proprietary software optimized for their specific printer. But development of such software may not be a high priority for the manufacturer, in which case updates and support are likely be slow, and options for the printer limited.
If you feel that you're outgrowing your printer's proprietary software and you want to do more things with your printing, check out some open-source or free options. Open-source software is widely available and works on many different 3D printers. Since more people use this software, support information for the software is more readily available.
Internet Relay Chat rooms are a great place to find other people who can help you out. I've visited both the Solidoodle chat and the RepRap chat rooms when I couldn't find specific information elsewhere online. More often than not, the chats shed light on my problem.
Calibrate your printer
Printer calibration is the process of ensuring that your printer is doing what it thinks it's doing. For instance, it may think it's pulling 100mm of filament into the extruder, when it's actually pulling 110mm. This disparity would cause the printer to extrude too much plastic, making for less-than-optimal prints. So you must tweak the settings to tell the software what's really going on.
All sets of instructions should include methods for calibrating your printer. If yours doesn't, consult RepRap's wiki for a good set of generic calibration steps. (The RepRap wiki's general guidance will probably be a bit harder to follow than any instructions for your specific printer, but it's there if you need it.)
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