How do buffs and debuffs stack against each other?

When you are battling, buffs and debuffs are calculated the same way buffs stack with other buffs (linearly).

For example: If you have 500% Troop Attack buff and your opponent has -50% Troop Attack debuff, it doesn't mean your Troop attack buff will be 250%; instead, your Troop Attack buff will instead be 450%. On that basis, if you ever wish to analyze your own battle results, always calculate your buffs by subtracting their counter debuffs from them and see what amounts are left once all subtractions are made.

Remember that your base stats and your stat boosts (the non-percentage based ones) are calculated first before your percentages are added. Also,your opponent's debuffs cannot reduce your Troop stats to negative values. If an opponent's debuff is greater than your buffs, your Troops will attack with only their base stat value.