Power to Arrest
Who you are
A California security guard is a private citizen with a guard registration; the registration does not create peace-officer powers. Your arrest authority comes from Penal Code section 837, the private-person arrest statute.
The three lawful bases
You may arrest a person who commits a felony in your presence; a person you have reasonable cause to believe committed a felony even if you did not see it, provided a felony actually occurred; and a person who commits a misdemeanor in your presence. For the not-in-presence felony, both the belief and the actual felony are required-a mere rumor is not enough. After arrest, deliver the person to a peace officer without unnecessary delay and use only reasonable force.
Traps
Questions love to offer 'arrest for any crime' or 'probable cause' as the private-person standard. Probable cause is the officer standard; the statute says reasonable cause. Also watch: a guard generally should not search a person, and Miranda warnings are not required of a private guard unless the guard is acting as an agent of police. Store employees may have a limited merchant's detention privilege under Penal Code 490.5, but that is narrow in time and manner.
Rule of thumb
If you did not personally see a misdemeanor and no felony is involved, do not arrest-observe, document, and call police. When in doubt, the safer lawful action is to contain the situation from a distance.
Example: a guard sees a man take a bottle and walk past the register. That is a misdemeanor in presence; a lawful arrest is possible. If a customer merely says 'that man stole something,' the guard should not arrest on the statement alone.