The only way to get the BAT endowment is getting it from another user through tipping. There will also be options where you can get rewards by viewing ads but that has not been enabled yet. You can also get BAT through referrals if you will be able to get your unique referral link. The process goes like this.
- Install brave browser
- Register at Uphold and verify
- Register to be a brave publisher
- Link your YouTube channel to you brave publisher account to create your own referral link.
There is a limited option which social media platform you can link but hopefully they will support Steemit and the different condensers as well in the future.
BAT for STEEM is easy you just find a platform that supports them both I think Binance and Bittrex support them both have them exchanged there.