There are basically three ways to extend your WordPress blog’s functionality namely: 1) Find and install applicable plugins and/or widgets; 2) Write your own custom code by modifying the applicable theme files; 3) Hire someone one to do it for you.
By far the best way to extend WordPress is to find an already developed plugin, which adds functionality to the main content area, or a widget, which adds functionality to the sidebars. Functionality can be added for back end admins and authors and/or can enhance the front end user experience. Although I do much of my own customizations by modifying the code, I do it at my own risk and recommend that you don’t unless you’re very sure of yourself. Doing so is not for the faint of heart. If you do, you should at least make it a point to backup any files you change so you can revert back if things don’t work as expected. As for the third option, hiring someone, know that it can get expensive and that you should be very clear about your expectations and the competence of the person you hire.
One of my favorite extensions is H5P, which lets me create learning modules such as quizzes, videos, drag and drop, and matching games, among other things. Another is the D3.js library that allows me to create interactive visualizations. So far I’ve just played with it and have yet to learn how to adapt it to practical problems. Zotpress is another great plugin that allows me to cite sources and generate the related bibliographies for research papers.
Be warned, there are many many optional plugins and widgets to choose from. If you can think of some functionality you would like, someone probably invented a plugin for it. Be prepared to spend a lot of time evaluating each one you consider and make sure it has been tested with the version of the WordPress core you’re using.