Can you help me understand how to determine uncertainty of measurements and calculations?

I had a lot of trouble in my physics lab in college. One of my problems was understanding how to arrive at the uncertainty of my measurements and calculations. We didn’t really have to do this in high school, and they didn’t teach us in college, just kinda threw us in the lab and said “go at it.”

So say I have a length measurement that I’m finding with a meter stick. The meter stick’s smallest increment is millimeters. I measure something at 25 millimeters. So does that mean that the uncertainty of my measurement is +/- .5 millimeters, because anything between 24.5 and 25.4 millimeters will round to 25 millimeters? Or…what?

Then let’s say I have a calculation to make involving that measurement. For instance, say I need to find the slope of a ramp in which the previous measurement is the hypotenuse. So I also measure the height of the ramp and then use arcsin to find the angle. But what is the uncertainty of that angle? How do I incorporate the uncertainty of my measurements into my calculations?

It’d help me a lot to understand this better. Thanks.