iOS How to allow users to register an account / How to make a database of users

You could have a look at a service like StackMob.

This allows you to utilise server based services with no server-side implementation on your part.

These guys here: parse.com are doing a great job to facilitate developers the setup of a cloud database to do many tasks that are common in iOS apps.

In particular there is a section dedicated to user management (sign-up and sessions) that is well described here: Parse iOS guide

Finally the service offers some user interface help also, look here even if probably it is better to give to the UI some personalization by coding your own UI.

There are some implementations, but if your app is going to have custom code executed by server, you'd better make your own code.

Use a server side language (php, perl, ruby, python, java) to do the registration.

You'll probably need a REST service and/or json if you are going for easy peasy stuff (if you are to web apps programming). Otherwise, you'll need to do xml parsing and other stuffs. Use asi-http for the interactions between server and the app, or if you are using ios5.x it has already a json parsing implementation.