Twitter – How to see when someone started following someone on Twitter

To see all tweets, from anyone, directed to a certain user, you can simply search for "@username". For example, try https://twitter.com/search?q=%40codinghorror to see all replies to Jeff Atwood.

I think I originally misunderstood the question, here's my original response:

Yeah, person A's Twitter replies to person B (tweets that begin with B's @username) are only visible in the Twitter stream of those followers of A who also follow B. I think this feature is fairly non-obvious, especially for new users.

To my knowledge, the easiest way to see also the "@ replies" (without following the other user) is to go to the user's profile (at the Twitter website: http://twitter.com/username, or through some Twitter client) and see their full tweet list there. However, then you'll of course see "@ replies" to everyone, not just to the individual you were interested in. To put it otherwise: no, there isn't an easier way. To see full "conversations" in your feed, you'll have to follow both (or all) parties taking part.

When you follow someone, they can be alerted via email that you have just become their newest follower. In their settings, there's a section on Activity notifications, one of which is:

Email me when ☑ I'm followed by someone new

When they're sent this email, it prompts them to check out your profile. They can either leave it at that or follow you back.

Busy and famous people probably won't have this set up as it creates too much noise in their inbox.

If you want to reply to someone, you can check out one of their tweets and click the Reply link. That will give you a pop-up with their Twitter handle prefilled. Enter your reply and if you're not blocked, the reply tweet will show up in their @Mentions tab.

If you're looking to Direct Message someone, then they would have to follow you before you can do so.

If they don't reply or follow you back, and you haven't been blocked, they don't want to reply or follow you back.