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Do you like their music or sports performance? Make sure to stay on top of their latest productions and accomplishments by reading news sites that would feature your celebrity, such as TMZ, Perez Hilton, Yahoo! News, E! Online, and others. Subscribing to Google News alerts for emails about articles that mention your celebrity is also a good idea. Make a note of what organizations and charities the celebrity is involved with. Follow them on Twitter and stay on top of their work as well. If it accords with your personal beliefs, you may even make a donation to that charity and let the celebrity know. Use hashtags that they use and are trying to promote. Retweet their tweets to your followers, especially when they are asking fans to check something out or are promoting another entity. Reply to their tweets with your reactions and thoughts. This will flood their Twitter streams with comments from you, making them more familiar and comfortable with you. As a result, they may start following you.  Don't be annoying. Remember that they are human beings, and don't like to be spammed or to receive the similar overexcited messages repeatedly. Make sure each interaction you make with them is meaningful. Time your engagements well. Responding to every single one of their tweets comes off as desperate and fake. Only respond when you have something interesting to say or when you really want to get their tweet out to others. Engaging with them more than twice a day borders on excessive. When your celebrity accomplishes something or does something praiseworthy, tweet at them to congratulate them and express your appreciation for the work that they do.  Make sure to time it appropriately—hence the importance on staying up-to-date about the latest news surrounding your celebrity. They're human beings too; they would appreciate a compliment on their new album or hairstyle just as much as the rest of us would. Ideally, you want to produce an emotional reaction from the celebrity to your tweet. If you liked their new dress, say why or talk about an outfit it inspired you to wear. Feel free to include photos! If you enjoyed their entire new album, say that it's been playing on repeat for the past 13 hours. Make sure what you're saying is true: celebrities can tell when someone is being over-the-top and brown-nosing for attention rather than expressing genuine appreciation. If you can get a laugh out of somebody, they like you better already and are almost certain to reply. Don't force it, but some of the tweets you make to the celebrity will naturally lend themselves to a further question, which will encourage the celebrity to reply back to you. For example, you can ask when their next tour is coming up, or what their favorite piece in their new fashion collection is. Make sure your question doesn't require a lengthy response, as Twitter only allows 140 characters per response. For example, a question about the source of inspiration for a song would be a better choice for an email or direct message on Twitter than a tweet. Try tweeting to your followers about the celebrity. Be sure to tag them at the beginning or end, and only say nice things. Celebs don't want to see their name attached to a hate message. You can also tweet out to your followers to follow the celebrity. For example, you could say: "@celebrity is only 10 followers away from getting to 12K! Hit that follow button, sweethearts!" Celebs love it when their fans help them gain more followers. This usually works, and it's amazing because the celeb will have more followers, and they may even tweet you thanks (or follow you).

Summary:
Reflect upon why you are a fan of this celebrity. Involve the celebrity in your tweets. Tweet @ the celebrity! Use humor and wit to make your tweet stand out. Ask a question, when possible. Tweet to your followers.