You can invite the person through the chat system or by leaving a comment. Note that a user needs at least 20 reputation to be able to chat, so check that first.
Note: Stack Exchange has three different chat sites -- one for Stack Overflow, one for SE Meta, and one for everybody else. In the following explanation my links are for the last (chat.SE); if you're using one of the others you'll need to adjust that.
First, go into chat and enter the room you created. (This is important; you can't invite someone to a room you're not in.)
Next you need to find the user's chat account. Go to the chat users page and search for the user's name. Note that some users use different names on different sites and some don't have chat accounts, so this isn't guaranteed to return a result.
Let's suppose I want to invite you. On the chat user page you'll see several buttons, one of which is "Invite this user to" and a drop-down list of all chat rooms that you're in.
Select the chat room and click the button; the user will be pinged. Note that it can take 20-30 minutes for the ping to arrive, depending on how recently the user has been in chat.
Then monitor your room and see if he responds.
If you can't use chat directly, you can leave a comment inviting him into your chat room. Create the room, enter it, get its URL, and then leave a comment addressed to the user and including that link. This is, by the way, more public; anybody who sees the comment might choose to come into your room. But almost nothing is really private on the SE network anyway (for good reasons); I'm just pointing this out so you won't be surprised if it happens.