So if you have a frozen mallet and you attack someone (while you have red buff) or you use a slow like Nasus' wither, does it stack with the other slow?
Slow stacking in league of legends is rather complicated. But here goes:
Passive item slows (even if applied from different champions) do NOT stack. Eg. Rylais does not stack with Frozen Mallet.
Also exhaust and red buff slow do NOT with themselves. Eg. reapplying red buff won't snare for more than the first red buff slow. However, red buff does stack with, for example rylais scepter.
Active item slows and abilities DO stack. Active item slows are: bilgewater cutlass' active, hextech gunblade and randuin's omen. Here the rule is: The strongest snare counts 100%. Then the second strongest snare applied counts to 65%, and so on until 35%.
So if you use exhaust (40% slow) on a target with 400 movespeed, and then apply nunu's level 1 ice blast (20% slow), the slow will be:
1 - (1 - 0.4) * (1 - 0.2 * 0.65) = 47.8%
400 * 0.522 = 208.8 movespeed
I hope that didn't raise any more questions than it answered :p I can't make it any simpler, that's just the way it is calculated in this game.