How to wash sink for sink laundry?

Hi I’ve seen lots of detailed guides on how to do sink laundry but I wonder how do you wash the sink itself before you start? I feel put off by imagining myself brushing my teeth and spitting out toothpaste in the sink earlier (or other people doing so at a hostel). At home, I use a sponge and cleaning products to wash a sink which doesn’t translate to being on the go. Thank you!