How do I build an app?

A website that sells clothing recently granted me full permission to make an app for them, and in exchange, I get paid a percentage of monthly sales. How and where do I start this? I started with conduit and actually created a good part of it, but when I add a part to "check out and pay", I have to put the link as it would appear when you're in your shopping cart. I want everything to be 100% done in the app. How do I start? Thanks.

 

A mobile app? Could you provide a few more details please?