Having recently gone through this exercise on my '57, I would add a few things to that article.
First - speedometers should be lubricated with clock oil, not WD-40. I bought a spray can of clock cleaner and small bottle of clock oil off eBay for a very reasonable price.
Second - be very, very careful removing the needle. Carefully twist it counterclockwise. If it doesn't want to move, hold the speedometer face down, put a drop or two of WD-40, Liquid Wrench, or PB Blaster on the shaft, and let it soak into the shaft/needle joint. Wait a few minutes, then try again. It'll come if you're patient.
As you take things apart, keep a sharp eye so you don't lose the tiny jewels on the shaft. It's best to disassemble things with the speedometer face up.
Soak the daylights out of the thing with the cleaning solvent. Let it dry, and carefully oil all moving parts. If it's still sticky, you may need to disassemble the magnet/wheel assembly. It's incredibly easy to break things doing this, so do it only as a last resort.
The magnet/wheel need to be carefully aligned so they don't drag when the cable connector is spun. Start by getting the shaft approximately in the middle of the outer wheel, and tweak as needed. Hold the speedometer facing you. When you spin the cable connector (clockwise) quickly and let go, the wheel should return and bounce a couple of times as it hits its stop. There should be no noise while doing this.
Hope this helps.
