I have to make 100mL of 400mM NaOH. How do I go about calculating what I need to prepare this?
This is relatively easy. First: Look up the molecular weight of sodium hydroxide: Wikipedia gives a molar weight of 39.997 grams/mole (lets round this to 40 g/mole thats easier to calculate and the error in this is marginal).
So when you dissolve 40 g of it in 1 l of water, you have a 1000 mM (or 1 M) solution. Since you only want to have a 400 mM solution, you need to multiply the final concentration with the molar weight to get the amount of NaOH for one litre: 40 g/mole * 0.4 mole/l = 16 g of NaOH per litre. Since you only need 100 ml, you only need 1/10th of the NaOH (1.6 g).
So to prepare 100 ml of a 400 mM NaOH solution you dissolve 1.6 g of NaOH in 80ml of water and fill up to 100ml in a appropriate messuring cylinder.