You'll need a little more detail than that to get a useful answer, unfortunately.

Are you a developer and/or someone with access to custom development? If so, there are great options like Stripe available. You can use PayPal's API.

If not, you may want to look into SaaS offerings that handle the UX for you.

Also, is this a native mobile app, or a web-based mobile app?

Do you need subscription payments or one-off payments?

Taking people's money online is a complicated, risky process that needs to be extremely well-considered. Otherwise you risk big problems: unhappy clients, security vulnerabilities, poor usability, and so on.

I would recommend doing a good deal more research on your own, then coming back to this question with far more detail.

Good luck!