The laws define a psychic call as a "deliberate and gross mis-statement of honour strength and suit length." The right to make such bids is guaranteed by Law 40A:
Law 40 - Partnership Understandings
A. Right to Choose Call or Play
A player may make any call or play (including an intentionally misleading call - such as a psychic bid - or a call or play that departs from commonly accepted, or previously announced, use of a convention), without prior announcement, provided that such call or play is not based on a partnership understanding.
So, there is really one more part to the definition of a psychic call: it can't be part of your system, but rather is a deviation from your system.
There is no set rule saying "you may psych on at most one hand out of ___." There are, however, two things in the laws that control the frequency of psyching.
One is the requirement that a psych not be "based on a partnership understanding." If you psych repeatedly in the same situation, your partner can't help but notice the pattern. Psychs by their nature tend to be rather spectacular and memorable things, frequently leading to surprise tops or (more frequently, for most) bottoms. It's very easy for your partner to -- consciously or subconsciously -- change his bidding style to accommodate your habit. Once partner does this -- say, by giving only a single raise even on hands that are worth a jump to game opposite a partner who can be counted on to have his bid -- your system has changed to adapt to the psychic bid, and your tendencies in psyching now have to be Alerted and explained just like any other nonstandard partnership agreement.
In many areas of the world, such an agreement will run foul of the system regulations. Sponsoring organizations have the right to forbid you from systematically opening hands of less than 8HCP at the 1-level. They may also forbid you from using conventions which you employ to identify psychic bids and escape from an otherwise-forcing auction ("psychic controls").
Secondly, if your only reason for psyching is purely destructive -- to harass your opponents or disrupt the game, as opposed to a sincere attempt to achieve a good score on a board by unorthodox means -- you will be violating the Proprieties. Bidding 7NT on six points "just because we are losing anyway and I've never lost 24 imps on a single board before" will get you in trouble for disrupting the game, just like walking out of the game early or getting into a shouting match with your opponents would. If you make a habit of psyching excessively often, you may find the director asking questions about why you psyched, investigating to see if you were playing bridge or causing trouble.
This doesn't mean that a psychic bid is illegal just because your opponent is upset at being misled. A deceptive bid is a legitimate way to try to get a good score on a hand. It's psyching just for the purpose of upsetting the opponents, not trying to win, that isn't allowed.
A psych has to be a deliberate and gross mis-statement of your hand. An accidental mis-description of someone's hand, either as a result of a misclick or of forgetting one's system, is a common accident. The end result of a misbid is much the same as for a psych, in that there is generally no automatic penalty, but the misbidder gets whatever score they earn, for better or (much more often) for worse.
Mild distortions of your hand shape or strength are not psychic bids; that is just trying to find the best bid within your system for a difficult-to-bid hand. For example, some players will open 1
instead of 1
holding 
xx 
Kx AQJx KTxxx, because they foresee a rebid problem if they blindly open their longest suit. (If a player does this every time he holds 4-5 in the minors, he should include this in the explanation of his 1 opening; but if this is only an occasional deviation, he's within his L40A rights.)