On your resume, the first section should list your technical skills, education, and any certifications. Programming languages, databases, platforms, OS's you're familiar with, integrations, APIs, etc.
In the next section, instead of a work history (where you would normally put a succession of programming jobs that you've had), list all the projects you've worked on. Describe what each project did, what you accomplished, and the tools/languages you used to accomplish it.
Create a professional portfolio website that showcases the projects you did, ideally as working demos/prototypes. Then put a link of that website on your resume (in your contact section).
When they ask about the gap, just be honest.