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Determine if this is the right time to approach them. Casually approach them and say "Hi. Make a personal connection. Ask for an autograph or a picture if you want one.
Remember that celebrities are people, too. They will have times when they are busy, frustrated, or otherwise dealing with a major situation where it might not be appropriate to approach them. If you see a celebrity who seems like they're in a big rush, or if they are dealing with a critical situation, leave them to their business. Some situations, such as escorting someone into an ambulance, will be obvious. Others, like if they are in a rush while getting coffee, will be less conspicuous. Use your best judgement and respect their time and space to the best of your abilities. Try to make eye contact and smile at them. Not only does this help give you confidence, it gives them a chance to acknowledge you. If they don't acknowledge you, they may be too busy. " Try to stay composed. Don't panic or start screaming if they wave or smile back. Simply casually walk up to them and introduce yourself. Say hi, and let them know that you're a fan of their work. You could say something like, "Mr. Johnson! I can't believe I'm meeting you in person. I've been a fan of yours for a long time." If you know they have just had a widely publicized life event, such as getting married or welcoming a new child, you can say something like, "Congratulations on your marriage!" Stick to widely publicized events. Do not drop personal or private information that you learned online or through gossip magazines. If the celebrity's body of work has had a major impact on your life, don't be afraid to let them know. Otherwise, try to make a personal connection by talking about things you would talk about to any other person. Ask them about their work, and let them know why you're a fan of them. Try something like, "Your second album was really important to me when I was applying to college. It helped get me through some very stressful moments." Remember to keep the conversation brief. Let them know that their work helped you through a hard time, but don't give them a long story about your life unless they specifically ask for it. Keep things short and sweet. End the conversation with something like, "I know you're busy and I don't want to keep you. Thank you for taking a few minutes to talk to me!" Celebrities know that things like autographs and taking pictures with fans are part of the deal. Don't be afraid to ask for a quick autograph or picture if you want one. Just make sure to keep it quick, and always ask their permission before you take their picture. Don't get mad if they won't give your their autograph. If they refuse, say "That's okay. I still enjoyed meeting you. Have a nice day." A graceful ending is always best. Some celebrities may take a picture or sign an autograph, but may ask you not to do something like post the picture on a certain social media site or to not get their autograph tattooed on you. Respect their wishes in these cases.