Wonder Guard prevents damage from direct attacks unless they are super-effective. Shedinja is the only Pokémon with this ability, meaning only Fire, Flying, Rock, Ghost, and Dark-type moves will have an effect.
However, Pokémon with Wonder Guard are not immune to indirect damage. Status moves still work, and end-of-turn damage like poisoning, burns, sandstorms, or hail will still apply. Entry hazards such as Spikes or Stealth Rock also damage Pokémon with Wonder Guard when switching in. Attacks that do not consider type, such as Struggle, Beat Up, or Future Sight, will also hit. Since Shedinja only has 1 HP, any such damage results in an instant knockout.
