I won't create an entire demo on it, however I can give you a brief explanation as to one to go about it.

You will want the skilltree window created in the skin ahead of time. Here, you can create a separate map feature where you will later on display the available skillcards using BYOND's new multi-map feature.

Have a way to call up the skilltree window using winset, and once it's opened, have it display all of the skills in the second map element. This can be done numerous ways, the easiest would be setting up a screen loc for each skill card and placing them at that location. You can do the same for any arrows or however you want to connect the skill tree system, which can be done the same way as the skills.
You may or may not want to devise a universal layout for the connectors to go in case you want multiple classes, or you can check for the classes and place them according to predefined locations based on the class.

Make each skill card clickable, running a generic proc which should check for requisites(if() and list() helps bunches) and then create the new /obj/skillcard in the user's contents.

I don't know where my reply went, but if you want to find a "skill tree" demo, just use the Search boxes which should be located in the top-right of your web browser. Since you are in the Developer Forums, there should be 2 boxes visible. One for searching all of BYOND.com, and one for being more direct and searching just the Developer Forums.

Searching "skill tree" in the BYOND.com search-box turns up handy articles and even 2 demos.

EDIT :
For "recommended" demos, they would be labeled with a Star with the hover-text of "Favorite resource".
These are either ones you have favored or ones that are top-notch quality of BYOND throughout the time.
Ones without the stars fall under the "Use As-Is, No Guarantee."
These are ones where you would ask for personal opinions or try them out yourself.