Quote or tag them and ask them questions about what they said (if appropriate). Show interest in what they have to say. Be friendly. Thats all you can do from your end, how they interact with each other is up to them.
Asking open-ended questions is a good way to keep conversations going.
Have the forum moderated well. Nobody likes going to a forum where members are berating one another & the admin is nowhere around.
Make them feel at home. Like they are more than a number to your forum. Members will be more apt to stay around & talk with one another.
I don't encourage my members to interact privately, I believe every opinion should be exchanged in a public forum. In my experience, private messaging triggers spam and scam.
Plenty of new activity with open-ended questions asked in threads is one way to get members to communicate with one another. Quoting a member and interacting with them also gets communication going as well I feel. Posting threads with questions so the members can answer and quoting them asking more questions related to their answers is another way I have found to get members communicating as well.