Transferring ownership of a dataset is very easy to do through the Manage tab on a dataset.
What does it mean to "transfer ownership?"
Transferring ownership means that you are changing the owner of that dataset. This is different from sharing a dataset, which shares the dataset with other users while retaining original ownership. For more information about sharing a dataset, read this article.
What rights do I need to have to transfer ownership?
You must be an administrator on the site. Furthermore, the person to whom you are transferring ownership must have an account on the Socrata platform. If you are viewing another person's dataset you will also have the option to transfer ownership to yourself.
Transferring ownership of a dataset is now done through the action bar. First, select "..." in the bar and Transfer Ownership.
This will open a modal where you can type in the name or email of the registered Socrata user you would like to transfer ownership of the asset to. Once selected, select Transfer.