Wow, I could use this as a cheat sheet at conferences:

"Get the person to introduce you to someone else. This is a good method for networking-type events. Ask the person if they know someone that can help you with a problem:

• Do you know anyone who’s dealt with the guys who run ___?
• I’m really interested in ___? Do you know anyone with experience in that?
• I’ve been wondering how to get started with ___? Do you know anyone who’s done that?
• Can you suggest anyone who could help with ___?

If your conversation partner does know someone who can help with your request, they’re likely to take you over to meet him or her. If they don’t, you can simply say, “Well, I really need to find someone who can help me with this. I’m going to ask some more people.” Either way you’ve just smoothly extricated yourself from the conversation.

Invite the person to do something with you. This allows you to make a possible exit/continue on to what you wanted to do without your conversation partner feeling abandoned, and allowing them to still feel wanted. Say something like:

• I’m going to try to meet the speaker. Do you want to come?
• I’m ready for another drink. Want to go over to the bar with me?
• I want to check out the Cezanne exhibit. Do you want to go see it?
• Let’s check out the buffet.
• My friend Mike just walked in. Let’s go say hi to him.

If the person declines your invitation, well, you’ve successfully ended your conversation with them. If they accept the invitation, you can hook up with some more people who can liven things up, and you can keep after whatever your original agenda/purpose was before you got pulled into the conversation."

Much better than "Bugger off, mate!"

MUCH better than "Bugger off, mate."

These phrases are useful!

This one's my favorite:

End with appreciation. Whichever of the above methods you employ to exit a conversation, end the interaction with appreciation. Small talk expert Debra Fine calls appreciation “a compliment with closure.” Recap the conversation in a positive way, thank the person for giving their time, sharing their expertise, or simply being fun to get to know, and be sincere – only say it if you mean it. Use their name too – it builds a last bit of rapport (and it helps solidify their name in your memory if you just met them). This kind of goodbye ensures you go out on a high note, with warm feelings between you.

• Thank you for sharing your thoughts on going to law school, Sean. It really helped me think though my decision
• It was wonderful catching up with you, Sarah. I haven’t laughed that hard in a long time.
• I appreciated getting your thoughts on the issue, Dan. I’ll take care of it as soon as possible.

If you didn’t appreciate the conversation, and don’t want to encourage the person to strike up another one next time they see you, just end with one of the exit lines above, and then a simple, “Okay, take care,” or something similar.

Maybe I usually on the other end of this challenge.  How to learn to be more sensitive to "the signs", since not everyone is this skilled and gracious in winding things down.

That's a good skill to practice, Tina.

Yes, thanks.  I've found that out the hard way!