+New dataset

While logged in to data.world click on +New in the upper right corner of your window to create a new dataset and you'll be prompted to choose either a dataset or a project:

Choose Create new dataset and you'll be prompted to name the dataset, and set the ownership and, accessibility. If you are in one or more organizations, by default the owner field will contain the name of one of the organizations you are in. You can also set the owner to be yourself or any of the other organizations you are in by selecting the dropdown on the owner filed: