First, schedule a call to talk with me about this so I can walk you through exactly how to connect with influential people. ;)

Next, always respect people's time. I've had the opportunity to connect with people that are very influential in my field and the number one secret is to respect their time. Even five minutes to read an email is a lot of time. Keep things short, and don't do anything that has the expectation of using any of their time.

Another way to connect is to offer suggestions or to participate in a conversation. Like, "Hey, I noticed this typo on your page. Not trying to be a grammar police but thought you might like to know." Or on Twitter, "Wow, loved your post on Inc. I really learned a lot. Thanks!" Being conversational like this without being annoying is good.

Asking questions is also good, so long as it doesn't require a lot of the readers time. People respond to questions on Twitter and via email more than anything else.

Last but not least, do everything without expecting anything in return. If you send an email with the expectation of connecting so you can get something out of the relationship, you're doing it wrong. You should be getting in touch without expecting anything in return.

Those are some of the things I practice and have found to work for me. Feel free to get in touch if you have more questions. ;)