Digital vs. Dial Calipers
Dial calipers use a mechanical system consisting of a rack and pinion, there's a gear-set inside as well that moves the dial in increments of one thousandth of an inch (or hundredth of a mm). To read, the 'most significant' value is read from the rule and the fractional value from the dial. The nice thing about dial calipers is that they don't use batteries and although are not waterproof, work well even if damp.
There are some downsides: if they are dropped, the rack and pinion can get out of alignment (especially on cheaper calipers) and it can be difficult to recalibrate. They're a little tougher to read and often are either imperial or metric (but not both).
Digital calipers don't have any rack/pinion/gear system. This makes them more shock-proof which we like (since we're a little clumsy and have dropped the calipers a few times).
Digital calipers can also easily convert from inches to mm and back which we really like since a lot of electronics is mixed-units.
This means that if the dielectric changes it can mess up the readings. For this reason, digital calipers can give jumpy readings if they are dirty or wet.
Battery Life & Replacement
Digital calipers do require a battery (there are solar ones as well, with an internal backup battery) but good calipers rarely need to have the battery replaced. The pair we have is used many times a day and often isn't even turned off for a few days but has been running without issue for over 5 years. We do suggest turning them off when not in use but many people don't even bother since the battery drain is so low.
To replace the battery, just snap of the top cover, the battery is LR44/SR44 size 1.5V button battery, available in any hardware or grocery store. The Silver Oxide SR44 costs more, but will last longer.
Setting the Origin
The first measurement is using the 'outer' jaws. Use the flat part if possible, to avoid any skewing. Use the thumb-wheel to get a good tight grip on the material. You'll notice it's not exactly 20mm, that's from the manufacturing tolerances, not the calipers.
The inner jaws are used to make measurements of slots and holes. These are a little tougher, make sure you're holding them so you are not getting an 'angled' measurement that is larger than it should be. I usually take a few measurements and also 'wiggle' the calipers to make sure they are measuring the minimum distance.
The last basic measurement is depth, often used for drilled holes. This measurement uses the gauge at the end of the calipers. You'll want to practice how to hold the calipers to push the tapered end piece down while also keeping the tail flat against the work, its a little counter intuitive!
Step & Relative Measurements
Say we have a mint tin that we're measuring. We want to know the thickness of the metal, but because of the rolled edges, there's no easy way for us get a good measurement with the outer-pincers. However, we can use two measurements and subtract them! This is what digital calipers are good at.
Step measurements are taken by pressing the 'head' against the bottom of the tin and then lining up the offset movable side so that it presses against the top of the edge.
Other Measuring Tips
We use our calipers to verify component sizes, sometimes these numbers are in the datasheet but once in a while we have a part for which the datasheet is incomplete or we just want to verify. If you're measuring a dense connector, its a good idea to measure over a large number of pins and then average.
For example, on this 37-pin FPC (flex circuit board) I'm measuring between the center points (as far as I can manage) of the two outer pins.