Connecting with people on LinkedIn is effective, but there is nothing better than making in-person connections with people who are in the field you want to be in.
Once you discover what you are really looking for in your next job, start identifying people you may know in that area who would be willing to conduct an informational interview with you. This will be an opportunity for you to ask questions about what the job would be like, what are the challenges, rewards, etc.
In addition to learning more about your dream job, you are strategically letting people know that you are looking and to keep you in mind if any opportunities arise. (Just make sure you don’t make your quest so public that your current company/manager finds out.)
And remember to send a thank you note to the people you speak with. It will show that you appreciated them spending time with you, and your ability to conduct business in a very professional manner.