You can get who is an subscriber in chat on TWITCHCLIENT 1 in a private message from jtv that has the form SPECIALUSER <name> subscriber. It also has some other additional information. On TWITCHCLIENT 3 it sends the same as a channel message, so then you have channel context which is necessary if you are on more than one channel to know which channel the user is actually a subscriber on.
To get new subscribers, you can listen for the channelmessage by twitchnotify that says <name> just subscribed! (or similiar).
You can’t get information about who is following via chat, so you have to pull the follower endpoint from the Twitch API for that. You can of course do the same for subscribers, but getting the list of the subscribers for a channel requires authentication from the broadcaster.