User Enters Prompt > Combine with Internal Prompt > Feed to AI > Return Results.
That's pretty much it but realize the "internal prompt" will take you months of work and refinement. There are many many tiny edge cases around using AI like this. One problem for example is you can tell the AI to return you it's data in a standard JSON object that you app can use, but if you set the temperature to high then the output will stop conforming. So you start having to do "pass-offs" between conversations with different temperatures.
And this is just one of a litany of issues around using AI like this. And really this is no different than a "traditional" SaaS app that doesn't use AI, I have a side project and that project has a litany of issues that must also be fixed.
Bottom line is building something like this is not any easier than building a traditional SaaS, just different flavors of problems.