You are arrested when you are taken into custody or when your freedom is restricted by a police officer. Sometimes arrest involves a search of your person or a "pat down" and handcuffing. Many times you will simply be instructed to accompany an officer to the police station.
If you are ever in doubt as to whether you are under arrest or not, you should ask the police officer. There aren't many magic words in law, but "am I free to leave" are close. Asking whether you are free to leave requires the officer to make a decision at that point whether they are detaining you. If you are not being detained, you are free to leave (and typically should). If the officer will not let you leave, then you are being detained, and a series of constitutional rights are triggered.