Everybody get ready to gasp in unison: I clean the brooder between batches of chicks.
I use the deep litter method even in the brooder, starting with the non-skid, non-adhesive shelf liner for the first day, maybe two. After that, I put down a layer of pine shavings. Any new, wet poop I see, I toss a handful of shavings over it. Every couple of days, I add more litter. If the chicks manage to knock over their waterer (if I am not using a nipple waterer for them), I will pull out the wet shavings and refill the void with fresh litter. They stay on this growing layer of pine shavings until it's time to put them outside, 8 weeks or so.
I will wipe down the interior sides of the brooder now and then, as necessary. I will clean - wash, not just rinse - the waterer every couple of days. Same with the feeder, if it has gotten poopy.
After the chicks are put outside full time, I dump the entire six inch deep layer of pine shavings into the compost, shake out the shelf liner, toss it into the washing machine, and then completely wash the brooder with hot, soapy water and let it dry in the sun.
Then I start all over again.