To do it, you need to be running Mountain Lion version or later. And you'll need to make sure you turn on Calendars & Reminders syncing in System Preferences -> iCloud.
In the Reminders Mac app, identify the list you want to share. Then move your mouse over the list's name in the left sidebar. Click on the broadcast/sharing icon that appears to the right of your list's name, and then fill out the field that appears with the name or email address of the person with whom you'd like to share the list in question.
Your contact will receive an email from Apple asking them whether they'd like to accept your invitation, including a warning that by doing so, they'll reveal their Apple ID to you. Once your contact accepts the invitation, you can both add reminders to your shared list from anywhere: Macs, iOS devices, or the Web. But you can only those shared lists on via iCloud or, now, with the Reminders Mac app.