This may be the most basic, but most effective strategy.

If you have some loyal customers, simply ask them for referrals of friends, co-workers, etc.

Sometimes asking someone to do something gives them a feeling of empowerment, and they'll gladly take it upon themselves to achieve their task.

Make it easy on them and only focus on your top customers. Unless someone loves something and can do it rather quickly, there's no real reason for them to do so.

Create a pre-written email for them to send and do something to thank them. It could be a discount for them and their invitee (read: Dropbox style) or it could be as basic as sending a personal thank you email that is sincere.

This also creates another bonding moment between you and your customer.

Also worth noting, this is a simple strategy that you can do manually, and if it works, then you can look into automating the process. It's imperative to really learn how and why your business works from the ground level before you automate a process or hire anyone else.