How do I download data on my mackbook pro to an external drive. Since my startup disc is full?

Plug in the external drive. It should appear as a icon in Finder and maybe your Desktop. Then just drag and drop files and folders onto the icon in Finder or your desktop.

Click here-> Use external storage devices with Mac - Apple Support

In addition to Phil0124’s answer and in case you have e.g. a large photolibrary, follow these steps to move it to an external drive https://support.apple.com/en-us/HT201517