The attack "Storm Hammer" says hit:1d8+_(wisdom modifier)lighting and thunder damage... how do I tell how much damage to inflict?
The amount of damage is equal to rolling an 8-sided die, and adding your Wisdom modifier to it. So for example if you have 16 Wisdom, your modifier is +3, and if you roll a 4 on the 8-sided die, you get 4+3 = 7 damage.
The type of the damage is both Thunder and Lightning. That is to say, for the above example, you do not deal 4 Lightning and 3 Thunder damage or something, it deals 7 (Lightning and Thunder) damage.
Multi-typed damage basically counts as whatever is best for you: the target uses the lowest resistance it has to any of the listed types.
So in the case of Storm Hammer, immunity to Lightning damage does no good: the creature would then have to use its Thunder resistance (if any). To be completely immune, the creature would need immunity to both. If the creature is vulnerable to either type, it takes that extra damage. If it is vulnerable to both, then it takes the extra damage from each.