How do Pedigree charts work?

The squares and circles that you mention are NOT STANDARD genealogy symbols. The core purpose of a pedigree chart is to show direct ancestry only, in a "tree" format.

So.. you are the root person to the far left... it branches into father and mother, going to the right. Each of those will again branch to show the father/ mother of those. Normally, the dates of birth/ death will be included just under the names.

The lines leading to father and mother are self explanatory.. no reason for any squares. Father is a male, mom is female.

The pedigree chart and family group sheet are the two STANDARD forms used. A family group is text based, dad/ mom at the top, with their details, including names (only) of the respective parents for each. Below, you list the children of that relationship only, in order of birth, with their facts.

I am guessing that what you have has been given to you, and is someone's own creation. The whole reason to use standards, is that they remain understandable by anyone, without the need for any explanation.

You can download PAF for free from the Mormons. It is to Genealogy what "Word" is to writing a novel. After you enter the data, you select an individual and print a pedigree chart - or charts, if you have more generations. It will print Family Group Sheets, too. It has other reports. Most of us don't bother filling in Pedigree charts any more. As others have said, you have a murky idea of a pedigree chart. On the simplest, you start with an individual on the far left, then put his/her parents on the two lines to the right, then grandparents, then great grandparents. Dads go on the top of each pair of lines, moms on the bottom. If there are multiple people in one generation you ignore all but one.