Please explain type effectiveness

When doing damage, your move's type. But you will get an additional 25% more damage if your Pokémon has the same type as its move is (STAB).

If you have a grass Pokémon, for example Exeggutor but you have 2 Psychic moves and you attack against water (weak to grass), you will get no bonus for your attacks (aside from STAB) because your attacks are both psychic and not grass types.

However, to incoming damage both your Pokémon's types matter but your moves do not matter. An Exeggutor (Grass/Psychic) will take 1.25 x 1.25 = 1.56 extra damage from Bug attacks because both Grass and Psychic types are weak to Bug.

Hope this clears it up for you, if not, ask me to explain in more detail :)

Example vaporeon is water type, so all water moves get 25% more dmg. (1,25x multiplier)

And you get another 25% (1,25x multiplier) more if you attack arcanine, cus arcanine is weak against water.

1,25 x 1,25 = 1,56
Total 56% more dmg vs arcanine.

Some pokemons have douple weakness.
Like Rhydon against water.
This means Rhydon alrdy takes 1,56x dmg
and vaporeons water attacks get 1,25x dmg

So 1,56 x 1,25 = 1,95
Total 95% more dmg against Rhydon

Like a Jolteon using thunder to a gyarados, does 1.25 (electric to water) times 1.25 (electric to flying) times 1.25 (STAB) equals 1 and 95.3125% total damage.