As far as brushing . . . it's important, but persistence is more important than strength. I've seen folks attack it, as if one really, really hard scrubbing would get it all cleaned up. No such luck! If you want to get rid of black algae after it's become established, you have to commit to approaching it as a long term problem. Think weeks, not days.
(Of course, many pool stores will be happy to sell you any number of products that promise quick results. And, they'll also be happy to explain -- when you don't get quick results -- why it didn't work for *you*)
What's important is brushing enough to remove any dead top layer, or at least to scratch it, and expose the live algae to the chemicals in the pool. But it's much more important to brush some today, and the day after and the day after that, than to brush really, really hard today.
Another thing you need to keep in mind: black algae doesn't grow rapidly, and didn't appear in your pool suddenly. It's there because, day after day, the chemical levels weren't right. And, once it's gotten a start, it's unlikely you will EVER get rid of all the roots and spores penetrating into your pool. (I'm assuming it's NOT a vinyl or FG pool??) So, even if you 'get rid of it' for now, it will come right back unless you learn to maintain proper chemistry day after day in the future.
Now, you didn't post test results, or tell how you've been treating your pool, so I don't really know what you've done wrong. There are numerous possibilities; here are a few of the more common:
Low, or inconsistent, chlorination.
High pH, not compensated for with higher chlorine.
High stabilizer, not compensated for with higher chlorine.
Poor circulation, or not running the pumps enough.
Porous or damaged plaster, not compensated for with higher chlorine.
Keep in mind that a single day -- or even week -- of one of these problems wouldn't lead to black algae. It just doesn't grow that fast.
So, what you really need to first, is figure out what's been going wrong, and learn how to correct that. Otherwise, anything you do to get rid of the algae will be only very temporary in effect! Fortunately, as many PoolForum members can tell you, doing it right is easier and cheaper than doing it wrong, once you learn how!
Meanwhile, except for the trip and fall hazard from the black algae, there's no reason to not use the pool while you work on the problem . . . as long as you have chemistry that's adequate for sanitation
Once you figure out what you need to correct, and take care of that, the solution is pretty straight forward:
Brush regularly.
Maintain chlorine levels 50% higher than you'd otherwise need to maintain.
Using polyquat will help some, especially if you can FREQUENTLY brush hard. But, it's still going to take weeks, as a rule, not days.