Best way to go about storing data on the cloud

The general solution is to have a web service that you can access from your app. Communication is usually by http POST/GET and some kind of communication protocol. Most commonly NSURLConnection is used for this although there are some third party classes for doing http communication also. Depending on your app's needs the web service might be backed by a database or it might just write to a file or read from files on your site.

If you are a web developer or you know one you might develop your own web service and host it on your web site. If you don't already know how to do that it might be a bridge to far. It was for me. There are some commercial databases that provide web service front ends or web service communication protocols. These might be SOAP or REST. My experience is that SOAP is overly complicated and that REST apis tend to be straightforward to work with from a mobile app. YMMV.

One site I'm familiar with that provides a REST front end to a database back end is mongolab.com.