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?
Slowing effects follow particular rules when stacking:
If a champion is affected by multiple slows, the strongest one will be fully applied, while the others are applied sequentially with 65% reduced effectiveness down to 35% of its original strength.
Slow effects derived from items' passives do NOT stack, even when coming from different champions. Only the strongest item slow is applied at any moment. The exception to this is the active effect of Randuin's Omen, Hextech Gunblade and Bilgewater Cutlass, which stacks with other slowing items normally because they are considered champion abilities for slow stacking purposes.
Attacking a champion with the Blessing of the Lizard Elder buff when the target is already affected by that slow will reapply the debuff, resetting its duration. It will NOT increase the slow amount. The same holds true for the Exhaust summoner spell.
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.