They can attempt to send you BAT in the browser, but it shows that you're an unverified creator, so the browser essentially 'holds' the BAT and attempts to send to you for a period of time (I think 90 days).

You sign up at https://creators.brave.com/ for your website / reddit / github / twitter / soundcloud / etc and verification happens depending on the platform, then you're shown as a registered creator in the browser when someone visits.

You get the BAT donation and just like any income would have to consider tax implications.