Someone has to explain how this perk system works cause my head is hurting real bad trying to figure it out

You get one perk per level. You can choose to spend it, or save it for later. Every single perk costs one point, although some perks have up to 5 ranks. Each rank costs 1 point.
You must meet 2 requirements in order to qualify to purchase a perk. Firstly, you must have the minimum skill level in that skill. Secondly, you must have any prerequisite perks - i.e. the previous perk in the tree.
Im pretty sure that if you reach the top perk and that perk is connected to another perk below it that you haven't already picked, then your game would have had an error, since you need all perks below and connected to get the perks above.
Look at the Enchanting tree, as an example. He means, if you take the following route:
Enchanter --> Insightful Enchanter --> Corpus Enchanter --> Extra Effect, then are you able to take Storm Enchanter next, as it is connected to Extra Effect?
I don't think you can get Storm Enchanter without taking Frost Enchanter, and therefore Fire Enchanter. It'd be cool if you can go backwards though, there's no logical reason that I can think of why not.