Sometimes guys put too much pressure on themselves when they see a girl at a party or a group of girls at a party that they want to talk with. The first time you meet someone at a party, you have the perfect chance to get to know someone in a group situation without appearing to aggressive or threatening. Try getting involved in conversations with groups of people, and then if you and the girls hit it off, and you both want to, you can have a more private conversation out of the group itself during the party as well.
Set a reasonable goal when you first approach girls at a party. Do not expect them to fall in love with you at first sight, or the first time you speak. Establish a realistic goal in your mind of having a comfortable conversation with them.
Be polite. Do not barge into a conversation. See if you can catch their attention as you walk by. If you notice them looking at you, just say hello and see how the girls respond. If they respond back, ask an ice breaking question like "Are you having a good time?" From there, if they answer, you can start a casual conversation.
Look for your opportunity to introduce yourself, if step two does not present itself as an opportunity or it does not work. If you see the girls talking to someone else that you know, try walking over and either introducing yourself or hope that your friend will introduce you.
Avoid trying to dominate the conversation by talking about yourself. Talking all about yourself can give the girls the impression that you are egotistical and self absorbed. Instead, listen to what they say and ask questions or discuss the items that they are discussing. Showing interest in the information the girls reveal will indicate to them that you are interested in getting to know something about them.
Find out about their hobbies. This can be useful information if you decide that you want to eventually go further than just being friends, and might be interested in asking one of them out on a date. The more you know about the girls and the more comfortable they are talking with you, the more likely you are to have a successful conversation at the party.
Pay attention to non verbal clues. If the girls start to act bored, or like they have somewhere to go, do not try to make the conversation last longer than they seem interested. Remember, this is the first time you are talking to them, and don't expect to become best friends instantly. Ending a conversation with that little bit of the unknown left about you, might make you more interesting to them in regards to conversations later or even possibly a date down the road.