Much like uploading data, you can easily download small amounts of data through the site's UI, but if you're going to download large amounts of data, it is recommended that you use the CLI.
Download from Web UI
When viewing sessions in a project, you can select one or multiple sessions or one or multiple acquisitions. Once selected, you can choose the Download option from the Action menu. More details here.
When on the Project page, you have the option to download your entire project. More details here.
Exporting using the CLI
In order to download using the CLI, you'll need to first install the CLI. There are two main options using the CLI to get data out.
To download a "container" (e.g. project, session, or acquisition) or a single file, you'll want to use this option. Flags can be set to exclude or include certain files types.
This command is explicitly for exporting BIDS projects.