Firstly, talk about it. Mention it during game preparation. Find an article on it that explains it just right for your game, print that article out and pass it around to your players. Perhaps include it in your New Player Pack. Talk about its importance and that it’s the flipside to immersion. People can't manage it when it takes them completely by surprise. Then encourage people to talk to you about it.
It can help to provide a few anecdotes about your own experiences with positive and negative bleed and to encourage other experienced players to do the same. This will normalise the process.
Now is a good time to mention any disturbing content, triggers or likely bleed issues in your game. If characters can die at any time, if NPCs committing suicide is a risk, or if characters will occasionally aim to publicly humiliate each other to score points with the prince, then it's a good idea to let the players know. This helps empower them to know if this is the kind of game for them and, if so, the shared game contract allows them to prepare themselves for the worst.
I'd also recommend including some kind of gesture to reflect if someone is still feeling all right that can be subtly used in the game. It might be the A-OK sign that I flash you if I'm uncertain if those tears in your eyes are a sign of an enjoyable immersive experience or one you want to end.
Having a sign where people can cut the scene, take a step back for a few minutes, then narratively conclude the scene when it gets too intense is also a good idea for some games though naturally if it is used a lot by a particular player in a particular game in situations that are typical of that game than that game may not be suitable for them.
So now you've talked about it during the preparation phase, I'd also recommend mentioning it whenever you experience it during the game and to encourage other players to do the same. It doesn't need to be a big deal if you (or the player) aren't looking for reassurance. It could be as simple as an observation like: "Oh, felt a bit of bleed with that scene back then. All good now, though." Or: "I experienced more bleed from that than I thought I would!"
Typically people will discuss negative bleed as "bleed", by the way, and positive emotions by their named emotion. "That was so exciting!" or "I felt so good when that happened." That's fine and normal. People won't always want to explain precisely what painful or aggravating emotion they experienced, only that it did happen.
A strong social backdrop will really help as well. If you all go out for karaoke or meet up after game for food (eating together is a great social glue) then you will have a more positive network that will help people better identify bleed by divorcing the character actions from the player actions. In other words, if I only ever deal with your character, how could I know if you actually don't like me or are a mean-spirited person? If we've hung out together and had a great time, it's a lot easier to realise that it's a character event and simply bleed we're experiencing.
Finally after sessions if you have a heavy-bleed game having every player mention the most emotional moments they experienced during the game, either all together or in small groups (depending on game size). Mostly they'll focus on positive emotions, but do encourage them to at least mention if they experienced any bleed during the session, even if they don't want to go into detail with it.
So now that you've set the groundwork, what do you do when someone is experiencing painful bleed?
Firstly, validate it. Each culture treats reassuring and helping someone through painful emotions differently so go with a more sensitive version of that. In general, listen more than you speak and always validate what they're feeling. You can provide a few anecdotes of your own experiences but keep them short, sharp and shiny and don't let them take priority. In other words, your anecdotes are merely to show that you've been there and you understand rather than serving as a chance to vent.
Just don't give any anecdotes of when the same player caused you bleed as that can lead to a bitching session where you both rant about the player, and that's a very toxic way to go. If the issue is truly with the player, than it's not about character bleed and needs to be dealt with in other ways.
Gently providing perspective on the other characters' actions, or the GM's intentions, can help if the player seems frustrated as to why they were targeted in-character in such a way but should be done gently, in response to their queries, and without judgement. Re-iterate that they have the right to be upset, it's just that the other player didn't realise how much it would have hurt them or that the other character was operating on different information or had some other goal.
Oftentimes you don't have to give the game away in terms of character motivations, simply providing a half dozen different perspectives of what might be the case can help as it helps the player think in terms of IC motivation rather than OOC personality traits.
Give the player a bit of space to come to terms with their own emotions and then encourage the involved players to spend time together, especially if it's due to character antagonism. If they avoid each other than the bleed may become entrenched in actual resentment and that's the last thing you want. Depending on the players, they might be happy to have a special antagonist's hangout to have a bit of fun with it or they might prefer it to be a big group activity that's not so large they can lose sight of each other.
These are the techniques I've used so far, anyway. Does anyone know any other tricks?