In experimental physics, it is crucial to estimate measurement uncertainty and keep a log of such along with the log of measurements.
"Why?" This is important, simply because the point of the experiment is to make a conclusion. That conclusion needs to be verifiable by further measurement. If the uncertainty is logged with the results, and error is accounted during calculations, then the final result will be a range of numbers. If another experiment is conducted that gives a unique range of numbers, that experiment disagrees with the first result. If the two ranges overlap, they agree.
"So, how does one estimate experimental uncertainty?"
It may seem subjective, but each instrument has a tolerance specified by the manufacturer, which is measured statistically.
So, if you measured temperature with a thermometer that has a precision of ±0.5°C, that would be the ultimate place to start.
Other factors might cause the error to be larger than that, but such reasons should be recorded in the lab notebook.
For calculation, the general formula for propagation of experimental uncertainty in f(x1,x2,...xn) is:
Δf² = Σi=1..n (∂f/∂xi Δxi)²
This simplifies nicely for most simple calculations:
If f = x y, then Δf = f * sqrt(Δx²/x² + Δy²/y²)
If f = x + y, then Δf = sqrt(Δx² + Δy²)