Grab some paper towels.
You'll also want to have rubber gloves, and cleaning supplies for the tub, shower, toilet, mirror and counter. You can use vinegar and baking soda to do everything you need in the bathroom. This also saves on time and money. (However, if someone in your household is sick you will want to use more powerful disinfectants.)
1- Quickly take everything off of the counter top (put it away), lift the rugs (shake them out) and pull the garbage can and everything that goes on the floor and counters out of the bathroom. I just set mine outside of the bathroom on the floor.
2- Apply cleaning solutions in this order.
the shower walls (optional)
the tub (optional)
the toilet bowl See how to do this with baking soda and vinegar here
the toilet rims and base
the counter top
Vinegar water can be used on the mirrors, if you have glass around the shower it will clean that, on the toilet rims and base, counter tops, sink and the floor. I use the baking soda in the toilet and tub. See how to clean the toilet here. For the tub, clean it similarly to the toilet, just sprinkle about 3/4 Cup all over the tub and pour about 2 cups vinegar on top. It will fizzle up and clean well while fizzing.
3- Now work in reverse. Clean what you put the cleaning solutions on last. Grab a paper towel and clean the mirror. Then clean off the counter tops and the sink.