The best way to get recommendations is to give them. When you recommend a LinkedIn member you are attesting to their qualifications and people love being recommended. They will most likely reciprocate if you take the time to recommend them.
On a "what not to do on LinkedIn" note, don't ask people you don't know for references. I got an email message recently that said "I wouldn't mind a few words of recommendation if any of you know me." That's not how to ask for a recommendation, even if you know someone.