Hi Piotr.

Have anyone here tried to earn BAT tokens? From my understanding users can receive some small amounts for simple fact of using this browser, right?

As you can see in my post I have tried to win some BAT tokens and I have achieved it in a small amount. Those 157 BAT is a small amount, I have seen cases of people earning up to 300 usd per month. For this they must have a good portfolio of followers. Generally they are influencers, mostly youtubers who have many followers.

Can they be traded easily, for instance to STEEM?

Yes, they are completely interchangeable. I have never done it directly to Steem, but I have changed it to ETH or DASH and then to STEEM.

Would you mind explaining a bit how does this program works?

This referral program works as follows:

• You must first register as a content creator Here
  There you must place your channels where you create content. Youtube, reddit, twicht, twitter or with your own website are accepted.
  Once you do this you will receive your promotional links for referrals.

• Then, you must be ingenious to share those links with your friends and followers, so that they download Brave, install Brave and use it at least 3 times over the course of 1 month.

• When you meet these conditions, then you will receive a single payment for each referral, it should be about 20 BAT per referral.

For more information and resources, I recommend you join the Brave Community. There you will receive online response from the operators who are 24 hours willing to attend. On two occasions I used the community support and I was surprised by the excellent attention I received.

There are also FAQ

Your friend, Juan.