How To Integrate Web Applications into Existing Wordpress Themes

so this whole concept has been in the back of my mind for awhile now, but I haven't been able to figure it out. A google search of the question yields no useful information (for a beginner anyways) so I thought I should ask it here. When designing an online web service such as this or this creating the theme is no problem at all, and likewise creating the actual product isn't an issue either. My problem comes from actually integrating the two together. On a basic level I understand the verification process/registration of a user, but when it comes to testing the application before its release I am completely blank. I am also clueless on how, once the product has been finished, to integrate it into your product site (the bridge between your theme and the application). I'm assuming that you store the application in a file folder kept on your site, but is the actual display for the software just one big div? Or is there a function to call that would start the application? Totally new to this. Also, although I believe this question is acceptable and relevant to people in my position, I may be wrong. Instead of downvoting please comment that you do not believe it is a worthy question and I will remove it. Thanks everybody!