Tumblr provides a few ways to interact with people whose blogs you follow, both publicly and privately. The options you have available to you depend on which settings the bloggers have enabled. You can send asks and fan mail to communicate with someone privately, and you can comment publicly on a blog. However, Tumblr doesn't support private back and forth communication. To talk to someone privately, you'll need to send a new message every time you want to reply.
Reply to Answers in Public
Any post that you can reply to has an icon of a small chat bubble next to the reblog, share and heart icons. You can reply to most text posts and asks that are public, but not reblogged posts. Click the chat bubble icon, type your reply and then click the "Reply" button. The reply shows up in the post's notes as well as on the post creator's dashboard, where he has the option to reply to you directly.
Public Comment Requirements
To reply to a post, you must follow the blog that posted it. Some blogs may have enabled the option that requires you to follow the blog for two weeks before you can post to it. If you see other people commenting but don't see the option to do so yourself, you'll need to wait the two weeks before you can post. In some cases, the blogger doesn't allow people to comment at all. If a blog doesn't permit comments, you may contact the blogger through asks if this option has been enabled.
Reply to Answers In Private
When someone sends a private response to an ask you sent, there is no way to reply to it. To continue the conversation you must send another ask; there is no way to keep a private conversation going for more than one reply.
Asks vs. Fan Mail
Asks and fan mail are two similar communication options for contacting a blogger, but there are a few minor differences. Asks can be sent to anyone with asks enabled, but fan mail can only be sent to someone after following a blog for 48 hours. Fan mail lets you include links and does not have a character limit, whereas asks must be plain text and have a 500 character limit. Finally, asks can be answered privately or publicly at the discretion of the recipient, but fan mail can only be answered privately. In both cases, there is no way to continue a conversation after an answer has been received.
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