The bottom line is that you need to operate on LinkedIn as you would in the real world. Think of LinkedIn as just a business after hours ... one that has millions of people, goes 24-7, and allows you to learn about prospects before you connect. So do the same. Connect with new people. Reconnect with those you already know. But in all cases, find ways to help others. If you do those things (and are patient ... which is key), things will come your way.
To be more specific ......
1) Really understand who your target market is, so you can recognise them when you find them.
2) Really understand what it is you are offering to your target market - in terms of benefits, not features, so that they can recognise you when they find you.
3) Make yourself 'findable' by your target market:
a) Ensure your profile reflects both of these - who you are, what you are about, what you are offering and who you want to work with - with all the technical details Sian gives - keywords, call to action etc.
b) Participate honestly and fully in groups where you are likely to 'meet' your target market, or they are likely to 'meet' you.
3) Go looking for leads yourself. If you really know who you are looking for, and you are confident in what you can offer them, then use LinkedIn search capabilities to find leads for yourself.
Search for companies, find people you know at that company (or who know people you know - this is why you connect with people you 'don't know'), Find the groups they belong to. Make contact, start proper and honest conversations, send them a direct message.
If you show that you are really caring about your prospect and not just spamming them, then this will pay off.
Of course all of this takes effort and more importantly time .... so take the time to get it right.