The "how" is briefly explained in the instructions from page 14 onwards. In essence: Weight is measured; height is entered; BMI is calculated from those; body fat and water percentages, muscle and bone mass are calculated using a tiny electric current; I would guess the metabolic rates are based on average levels using all of the above plus the user's entered age and activity level(s).
It's not going to be entirely accurate, but if you're just using it for the purposes of tracking, I would say that it's "accurate enough". Essentially the values may not be exact for you, but assuming you're taking measurements at the same time of day with similar conditions (e.g. every Sunday morning before breakfast) then you should be able to track a downward trend to the results and see progress.
Also don't forget that numbers aren't the only side to the story. Regular progress pictures are a great way to see how you're progressing. For most people it's really less about the exact number on the scale and more about how they look and feel about the way they look.