Even without suspicion of wrongdoing, a police officer can approach someone and begin a conversation without violating the Fourth Amendment. As long as the individual reasonably feels free to end the discussion and walk away, it's a consensual encounter.
But in order to stop or "detain" someone, the police must have "reasonable suspicion"—an objectively reasonable basis to suspect that the detainee is or was involved in a crime. This isn't a full blown arrest, such as when an officer employs handcuffs and takes the suspect to the station. Rather, it's an interaction in which the citizen isn't necessarily accused of a crime but also isn't free to leave, at least until the officer indicates otherwise. (For more information on stop-and-frisk, see Police Searches on the Street: Stop and Frisk.)
An officer cannot frisk a detained suspect without a verifiable reason to believe that the person is armed and dangerous. But with that reason, an officer can pat down the suspect's outer clothing in a search for weapons—if the officer happens upon contraband (like a bag of cocaine), when conducting a limited pat-down for weapons, then it is presumptively admissible in a later prosecution. In that scenario, the officer would transform the detention into an arrest by further restricting the suspect's freedom by, for instance, using handcuffs and placing the suspect in a patrol vehicle.
An officer can arrest someone only with either a warrant or probable cause. Probable cause is an objective indication that it's reasonably likely that the person committed or is committing a crime—for example, if an officer hears and alarm and sees someone running from a bank with a bag of money. After the arrest, the officer can search the arrestee and the immediate surroundings.
For more information on how to determine whether you've been placed under arrest, see Arrest vs. Detention.