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Find a way to attend a party. Invite yourself to a party. Host a fun party yourself.
If you hear someone talking about a party, find out some details and try to get an invitation for it.  Ask a friend that you know is going to the party to hang out one-on-one at the time of the party—they may tell you about the party and invite you to go with them. If someone mentions the party, say "wow, that sounds really fun" and look them in the eye.  They will likely invite you if they are able to. Ask a friend who is attending a party directly if you can tag along. Show up to the party if you know when and where it is.  It is very unlikely that anyone will question you about who invited you. While this may not be as good as being invited, it may be a good place to start.  If a friend is attending a party but they are not sure if they can invite you to another person’s party, ask them to introduce you to the host. Start a conversation with the host of the next party, and then compliment them on their outfit or a recent accomplishment that you heard about (like being nominated to homecoming court). Casually ask them if they mind you dropping by her party for a little while.  Most people will be uncomfortable telling someone no to their face. Invite a lot of different people from different groups and tell them it’s okay to invite a few friends.  Be sure that everyone has a good time. Try to spend a little time with everyone who attends. Address everyone by name and thank them for coming.  Even if it’s someone you don’t know well, they will feel special if you pay some personal attention to them.  If you're not sure of someone's name, ask another party attendee who may know. At the end of your party, jokingly ask, “okay, whose turn is it to throw the next one?”