I think your easiest option is to utilise a third part form processor. Most of them allow you to design a form online and have it display in a pop-up or modal. This is something you can choose as part of the form creation process and will incorporate the feature into the embed code they provide you with.
To add the code to your page, you would add an embedded content widget to the page and paste the supplied code into the Embedded Content box in the properties panel.
The only issue you may have is triggering the pop up. This would normally entail creating a link or button in the page and then have that button activate the popup. Unfortunately, there isn’t a simple way to do this in Sparkle, so you should use a forms service that gives you the option of creating an activation link as well. This would be added to your page in the same way as the pop-up code.
Jot forms is one company that provides code for displaying in a light box. It also provides an activation link as part of the code.