How to Balance A Tonearm

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Here’s the quick and dirty process for balancing a tonearm.
I’ll start with a couple of definitions which may be obvious, but better safe than sorry.
Counterweight – this  is the extra weight on the end of the tonearm at the opposite end to the cartridge/stylus.  it’s purpose is to ensure the proper amount of weight is applied to the stylus as it rides the groove of the record.  Too much weight will cause premature wear of both your LPs and your stylus.  Too little weight and the stylus will not rest properly in the record’s groove and potentially skip or miss parts if the recording.
The counterweight must be adjustable because cartridges are not a standard weight.
Cartridge – this is the housing for the stylus, wire coil, magnet and the wires that carry the signals from the stylus and ultimately to your amplification system.  The cartridge is also the mechanism for securing the stylus, coil and magnet  to the tonearm.
Stylus – this is the point of contact between the groove of the record and also includes an arm or cantilever that conducts the movements of the stylus to the wire coil and magnet assembly.  The stylus is almost always made of a diamond or sapphire, but can also be made of steel, hardened steel or Osmium (Platinum Alloy).
So with these few definitions under your belt, here’s the six steps:
1 – Ensure that the guard or shield over the stylus has been removed.
2 – Ensure that the anti-skate is set to zero.
3 – Take the tonearm off its resting position and adjust the counterweight so the tonearm balances horizontally.
4 – With the counterweight balanced horizontally and still, set the counterweight scale to zero.
5 – Now turn the counterweight and scale to the desired tracking force.  Each cartridge will have a recommended tracking force.
6 – Set the anti-skate to the same value as the tracking force. 
For a good video, try this one by Pixelriffic.
And here’s some excellent detailed instructions from the Vinyl Factory.