How to create LUIS application that can be accessed through my organization account?

I am using LUIS to extract intent for the user utterances. I have did it through my own free Microsoft account. Now how can I get a organization subscription? Is it free like the normal Microsoft account or billing different for the organization or enterprise accounts.

The documentation was not clear about the billing. Also I am new to Azure.

If this is something you are doing for your own business, then you can convert your free account to a Pay-As-You-Go account. Instructions are available here

If you are doing this for your employer then they would need to provide the subscription information to you and grant you contributor access.

The image in your question isn't really related to subscriptions or billing. Did you intend to include it? What the image is talking about is the active directory consent. Basically, your Luis app needs certain AD permission to do stuff, and only someone logged in with the correct privileges and 'consent' to granted them. The consent framework is a pretty large and important topic. Here is a great place to get started.

I hope this helps.