Hi everyone, I can see I'm wanted!
I've been very active at LinkedIn for over a year now and spent Easter 2007 exploring, reading, and trying things out. Today I have well over 1,000 first level connections and over 7 million 3rd level connections - believe it or not most of that has occurred through people inviting me and not the other way around. How did I do that and make people want to connect with me? Simple, I worked the system and networked. Here's how I did it:
1. Explore what your LinkedIn page has available for you. To save retyping it, go to
http://soho-life.com/blog/category/linkedin/ which is one of my blogs and the LinkedIn category there will show how to use LinkedIn and the benefits. In fact go back to the first page of posts in that category (at the bottom of the page there is a link for the next page) and work back to the latest ones which will give you an idea of some of the journey I've gone through.
2. Build your profile and make sure it's complete - I've seen so many empty ones. How is anyone supposed to know what you do unless you tell them? See mine at
http://www.linkedin.com/in/kathiethomas and yes, I do welcome invitations. Note that your profile should be kept up to date as the search engines do pick it up and for many people, their LinkedIn profile shows up in Google long before any of their other websites. This is a good reason why you should be using a linkedin address with your name - there are instructions on the site how to do this.
3. Make your presence known at the LinkedIn site. Answers is the best place to do this as it doesn't have an interactive forum like this one. So what you do is answer other people's questions and place some of your own - you have a limit of 10 per month, believe it or not, some months you will use that up. Answering or asking questions will put you in front of a lot of people at LinkedIn who don't know you're there and they will go visit your profile (which is why it needs to be complete and up to date) and often you'll start receiving invitations from others.
Now, don't make the mistake of thinking that all those connections are going to make something happen - in most cases it won't. Many people are into quantity and not quality over there. Their excuse is that they want to connect to as many people as possible, just in case... They think having big numbers in connections makes them big - it doesn't, unless they're proactive and many aren't. So, what's the answer? Well there are a few things you can do.
1. Download your entire contact list in csv and send periodic emails to your list but don't add them to your newsletter list or anything like that - you'll lose connections quickly and/or get reported for spamming. But you can at least start to explore what people do and when you're looking for something you can send them all an email outlining what you're looking for (a bit like using Answers but you have more flexibility and direct contact).
2. Join any number of forums run by LinkedIn members. I belong to a few other groups too and you should be able to see the list on my profile - you can just click on each one to read about it and ask to join.
I don't answer everything or join in everything at Answers or the forums but I do participate regularly and have picked up many new clients, new members for my VA team, and found resources for all sorts of things. And I get lots of people emailing me for advice - yesterday a guy from MLPF sent me his resume asking if I would give him an appraisal (good try - wanted something free, I think

) but I advised that wasn't my expertise but I do have some VAs who specialise in that and I could let them know so they could advise their fees. I also get men emailing me asking if their wives could do what I do, or how do they get a VA, and so on.
You'll also note in my soho-life posts that I host a LinkedIn Blog Carnival monthly - this grew out of connecting with lots of bloggers and deciding to find a 'home' for them to showcase their blogs - many are now getting involved with some starting to put their hands up to host a carnival.
When exploring and connecting with people you'll find there are lots of discussion forums on many, many topics so feel free to join ones that interest you - some are very active, some quite quiet.
Anyway, that should give you some idea of how it works and set you off in the right direction!