When entering into battle against Psychic-type Pokémon, it's worth knowing what their weaknesses are. Psychics are weak against Bug, Ghost, and Dark-type Pokémon. Dark types are especially useful, since they are immune to psychic movements. Even some of the most fantastic types can be deduced this way.
Take the fairy type, for example. It is strong against the dark guy, which makes sense if you consider the traditional archetype of fairies in fantastic literature and cinema. In the same way, ghost types are effective against psychics, and dragon types are weak in the face of fairy attacks. Poison-type Pokémon are also vulnerable to psychic movement, so you might leave them inside the Pokeball when you're in battle.
Fighting psychic Pokémon can be difficult because many of them are legendary Pokémon or hit with the same force. Of course, this also means that it makes little sense to bring a Psychic Pokémon to fight another Psychic Pokémon. Many Pokémon are of this type and, being the type with the most legendary Pokémon, for many, the Psychic type is the most powerful. Psychic damage is not elemental, but Psychic-type Pokémon can also use elemental moves along with their psychic moves.
In particular, every psychic attack introduced before the fourth generation was still a special attack, physical psychic attacks were only introduced from the fourth generation. For example, ice types are weak for steel attacks, for some reason, and insect attacks are super effective against psychic types. A psychic-type Pokémon is any Pokémon that specializes in certain moves that use psychic themes to damage or inflict status effects on an opponent. The fraction of damage that will be inflicted by a psychic-type move is shown: ½ means 50% damage (not very effective), 2 means 200% (super effective), etc.
Also, an in-game bug meant that Ghost moves had no effect on Psychic (although this only affected the low-powered Lick).