How much you have to do depends on where you work.
A lot of places have drug sheets or equipment (monitors/pumps) to do the heavy duty calculations for drugs like dopamine or Versed drips. Otherwise, you use formulas (lots of us carry little books with formulas and other info) and your trusty calculator. The every day NICU routine involves a lot of checking safe-dose ranges for the baby's weight (and sometimes age) with the drug order, and calculating the quantity of the drug to give (usually mg ordered divided by mg per cc of concentration available.
You will need to be able to understand and figure out the urine output in cc/kg/hr, the total intake (cc/kg/day) and in some places calculate the kcal/day. As more NICUs go to computerized charting, a lot of this stuff will be done automatically, but you still have to know what it means and what it should be for each baby.
A really common calculation is IV+po. Fluid balance is very important in small critters, and they get a prescribed amount of fluids from all sources and if you go up on one you must go down an equal amount on another.
A calculator is an indispensable part of a NICU nurse's equipment. Any NICU that I've been in for the last decade has a policy of double-checking all meds with another nurse, so this minimizes the risk of error.
You do not have to be a math whiz to work in NICU but you have to understand the concepts of things like cc/kg/day and IV+po. In fact, I can't add, subtract, multiply or divide numbers larger than 5!
Just know that you have to be extra careful and use that calculator!
Best of luck to you.