Find files to print
Thingiverse, run by MakerBot, is an online repository of free 3D printable object designs that you can download and print them at home. People are constantly posting new designs and coming up with new and interesting things to print, like the Octavius Grabber Claw. It's wise to start with something simple for your first post-calibration print. (I like to use a cute waving octopus for my first print.)
You can find more than a few torture tests online, designed either to test the performance of a single set of settings or to combine lots of scenarios. The software must be able to account for things like printing tall pillars, bridges, overhangs, and small layer sizes, and printed them differently for optimal results.
Get a caliper
A caliper is a tool for performing highly precise measurements, down to hundredths of a millimeter (or even smaller). Having a caliper on hand will make calibrating your printer much easier, and it's essential for certain steps.
After measuring the exact diameter of the filament you're using, you can tell the printer its true thickness. The printer will then feed the filament into the extruder at the correct rate.
Filament diameter doesn't always measure up to what the manufacturer puts on its labels, though. Being able to measure the actual diameter of the filament at different spots, and then calculating an average of the actual diameter, will help make your printer that much more accurate. A caliper will also help you precisely measure calibration objects, to ensure that your printer is doing what it thinks it's doing.
Take it slow
It will probably take you some time to adjust your printer so that it delivers consistent high-quality prints. However, the time you take to tweak all the settings will pay dividends. A poorly calibrated printer might start a print just fine, but fail at a more complex point, or knock the model over halfway through.
If this seems like a lot to keep in mind, don't be put off. The adventure you have in setting up and calibrating your printer is rewarding, and you can often see improvements at once. Start by printing simple things, and learn as you go. And don't be shy about asking people for help (IRC chats for the win!).
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