Psyches are legal. They can be fun, and it is sad that some people get upset by them. It is much better to remember the saying: "Don't get mad, get even."
So if someone psyches against you, don't get annoyed, it is just part of bridge: perhaps you might try a psyche yourself next time you play against them!
Many of the psyches reported are not real psyches at all, but differences in approach. If an opponent opens a preempt against you on a five card suit, you may think he is mad, but if that is what it says on his convention card it is not a psyche but a difference in style!
Similarly, if someone opens 1NT on 11 points playing 12-14 it is not a psyche but a DEVIATION. This is perfectly legal unless he is doing it regularly in which case it is part of his system, and he should redefine his 1NT opening to 11-14 (or good 11-14, perhaps).
Psyches are deliberate: if someone makes the wrong bid by accident (perhaps because he forgot the system) then it is a MISBID.
There are some problems with psyches, which is why if you have any doubt you should report it to the Director. Psyches should be as much a surprise to psycher's partner as to the opponents. If partner's actions APPEAR to have allowed for a psyche then partner has "fielded" it, and that is illegal - even if he did not mean it! Always call the Director if you have any doubt about partner's actions. The Director will ask the partner why he bid as he did, and will then call it a RED psyche if the partner has fielded it. An example would be a player with 11 points whose partner opens in third seat and hears a 1NT overcall on his right. Now a double is automatic: anyone who passes APPEARS to have allowed for partner's psyche, and if partner has psyched it is RED.
If there are other possible explanations but some doubt the Director will decide it is AMBER. If, in the above example, partner bid 3 instead of passing or doubling, his action is strange, and the Director will call it an AMBER psyche.
In most cases where partner's actions are above reproach it will be classified as a GREEN psyche. If you are sure this is the case there is no need to even call the Director.
If a psyche is RED then the Director will cancel the result (unless the psycher got less than a 40% score) and will give the psycher 30% and his opponents 60%. If it is AMBER then he will merely take a note unless this pair has another AMBER or RED psyche in which case he will treat all future AMBER psyches as RED. There is no adjustment for GREEN psyches.
Should you psyche against weaker players? There is nothing wrong with psyching in general against players who may be weaker than yourself, BUT it is considered inappropriate to psyche against novices or beginners. There is no specific penalty for doing so, but if you do so continuously the club may correctly ask you to leave. But if your opponents are not inexperienced then it is perfectly acceptable to psyche against them.
Psyching is meant to be a method of trying to win. If a pair has lost interest in the competition and is merely psyching for the fun of it (typically on nearly every board near the end of an evening) this is unacceptable. In this sort of extreme case every psyche after the first two becomes AMBER and the club might tell the pair they will not accepted in the club if there is a repetition.
Frequent psyching is not a very good idea anyway because it becomes nearly impossible for partner not to allow for it, and the Director will make such psyches AMBER if he has the least whiff of suspicion. Any pair that regularly psyches twice or more EVERY evening might reasonably be asked to leave.
Assuming your club follows EBU or WBU rules then it is not allowed to psyche a near game-forcing conventional opening, such as an Acol 2 or a Benjamin 2 or 2. Also at Level 3 only you may not psyche the Multi. If anyone does then the result is scrapped and they get 40% and their opponents 60% (unless they actually got less when the board was played: the Director will always allow it to be played out).
If you do not psyche frequently, nor field psyches, nor psyche against novices or beginners, and do not psyche near game forcing conventional openings, then psyching is legal, and can be fun. Try it and see!
However, if your opponent psyches, don't worry or get upset: it is just part of bridge!