I wish I knew how to explain it, just how to use it. I'l try anyway.
Basically, you want to use your matches from GEDMatch first who you know for certain you are related to and on which ancestor, and shove the matches into DNAPainter by copying the table from One-to-One compare and filling out the information. Make sure you do this for your X Chromosome too, which has a separate compare tool, but it's easiest to add that information into DNAPainter at the same time as the autosomal information. Make sure you put whether the match is on your mother's (maternal) or father's (paternal) side.
You keep doing this with your matches that you know and can confirm, and you'll start to see the chromosomes get filled in. It shows you which DNA you got from which ancestor. Then you can look at people who you are not sure you are related to and add them into DNA painter as unknowns, and you'll be able to guesstimate which ancestors you might be related to them through just by looking at the DNA painting.