So given the NHS is now advising the use of these, I thought I'd explain how they worked (plus I've decided it counts as revision).

Pulse oximeters work on the principle that you if you shine a light through your finger, some of that light goes through your finger. https://twitter.com/beckymontacute/status/1347841965400973313
Haemoglobin is the oxygen carrying protein in your red blood cells and each haemoglobin molecule contains four iron ions that bind oxygen. Oxygen is also dissolved in your blood but haemoglobin massively increases your oxygen-carrying capacity. It's what makes blood red.
The pulse oximeter has a red and infrared LED (light-emitting diode) which emits what looks like red light. Infrared is not visible to the human eye (which is why you can't see beams of light go from your TV remote to your TV).
Those LEDs sit on one bit of the peg. On the other bit of the peg is a sensor which detects the levels of infrared and red light. "Infra" means below because infrared is "light" at a wavelength below red, the colour with the lowest wavelength.

Now the clever bit...
Helpfully, haemoglobin absorbs light at different wavelengths depending on whether it is carrying oxygen (ie whether it's oxygenated or de-oxygenated). The sensor detects the changing levels of light absorption and from that, extrapolates oxygen saturations.
In simple terms, deoxygenated haemoglobin absorbs more infrared light and oxygenated haemoglobin absorbs more red light. So if more infrared is absorbed, your oxygen saturation is lower, and if more red is absorbed, its higher. And that's how a pulse oximeter works!
And if you want some more practical tips (I've been using these things for more than 10 years), I replied to @beckymontacute's OP with this. https://twitter.com/rajacexplains/status/1347853439095758848?s=19
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