Need a process to get current clients to give us personal introductions to others
I have a slightly different approach than the listed ones.
The first one is set up a referral/partner network with associated documents, talking about what kind of business you are looking for, and most importantly, HOW MUCH will you compensate them for finding you a lead, and/or a customer.
But before you expect a current client to do that, you need to test their NPS (Net Promoter Score). After having some sort of "proof" with the client about your value proposition (in my case, after I bring in 10 leads and they make 3 sales or something like that), you should send them a really quick survey asking them how they would rate your service and how likely they are to recommend you to others. If they respond positively, email (or better yet call or sit down with them) and ask them if they know any other people that might be in need of your services, tell them of your referral program and politely push them to help you get in contact with the new prospect.
Hope that helped.