Joe Marr, has a great system for asking for referrals, called CAPS. The general idea is that you focus on some particular aspect of your target market which, when specified, is sufficient to trigger a listener's associative memory. Asking "Do you know anyone who needs a house?" isn't likely to stimulate any ideas, but asking "You wouldn't happen to know a young family who's about to have their third child, would you?" is more likely to get the desired results.
That's all well and good, and I hope you get a chance to talk with him about it sometime. Joe always has good stuff. The problem I always had was that getting to that part of the conversation always felt awkward. How, in normal conversation do you just drop in the request for referrals without it feeling like you are imposing on them?
Easy -- just have them ask you.
Wait just a minute, there, I can hear you thinking, How do I get them to ask me who I want for a referral? Is it some sort of Jedi mind trick? No, actually, it's simply a matter of helping them first.
I've written several times now about the importance of asking questions, and just as importantly, being ready to answer the questions you yourself are asking. So, in this case, just ask your listener who would be a good referral for them. After they tell you, around half the time they follow up by asking who would be a good referral for you.
Please remember a couple of things, though. First, you must ask from a place of sincerity. If you are just asking as a "technique" with no real intention of actually keeping this person in mind, that mendacity will show through. The second thing to be aware of is the other person might not remember after only one time who they should refer to you. Be prepared to "ask" several times. If you can refer business to them, they are far more likely to remember what it is you need, so be sure to keep tabs on what they need.
Asking for a referral is almost never easy, but if you show that you are trying to provide value to the other person first, you might not even have to ask. They'll ask you.
Just be ready to answer.