Standards, Prices and Mines
Most emotional issues that I come across in my own work are what I would call 'standards' issues. In other words, you're either putting up with something that you shouldn't have to or else you're expecting something unreasonable. A somewhat weaker form of this I call a 'price issue', ie how much are you "charging" or "being charged" emotionally for say friendship, love, sex, etc? With a full 'standards' issue it's not so much a matter of paying too much as it is expecting the wrong thing altogether due to, on some level, believing something that is false. Price issues are more negotiable, where ultimately you're looking for a fair 50-50 trade. This can happen when your 'parts' and another person's are in agreement regarding some primary issue, or if you've let go of your need for 'payment' in which case you can generally accept the other person's feelings.
In working with standards and price issues, the main thing you need to consider is what you're willing or unwilling to accept. It's a lot like Rosa Parks when the white person demanded she give up her seat. There's no such thing as 'compromise' in those sorts of situations, and either you'll be Rosa or you'll be the white person, and you basically have to decide whether or not you'll accept that role. In some cases, even though you'd rather say "no" (obviously, unless you like being a racist, which can happen to the best of us from time to time) you find that you can't congruently do it. This only indicates that you haven't navigated the issue enough to understand what the really important parts are yet. I call issues like this 'mines' like a land mine due to the fact that they can cause you to emotionally break down but the only thing you can do is dance around them until you've gotten far enough to dig them up and defuse them.
Inquiry and Acknowledgment
At any point in working with emotional issues you typically either know what to do or have no ground to stand on. In order to navigate from the latter to the former, you have to consistently reconsider what is important (ie what feelings, concepts, context), what that means to you or the other person (ie why is it important), and then what to do about it. What you do about something depends very much on what it means in the given emotional context.
With inquiry the idea is to try to untangle the mess that is your feelings, release the burdens they carry, if possible find out what your feelings are trying to tell you and eventually sort your way to freedom with the trail of hints you get. If your feelings are an impenetrable mess, you can either start by finding some way in which your standards (ie your constitution as a person) are being violated and then fight that, or you can try random things to find a positive response, ie some way in which your feelings can connect with someone else's. This is where inquiry and acknowledgment converge.
Once you have a starting point, you can begin to navigate your feelings to find out what they're about. Each feeling that emerges and which feels important is kind of like an item stuck on a shelf. The shelf may have various shapes and be at various heights, but in order to get the item off first you have to lift it, pull it away from the shelf, and then set it on the ground. This is how I typically experience the 'polarization' between parts described in IFS, and I've found that any part can carry burdens which include things like anger, sadness, jealousy (and arrogance), 'heaviness', specific complaints in the form of words, important ideas and occasionally more central (ie mine related) burdens. From time to time parts also reveal opportunities to 'open trade', when you can actually get back more than you've given without a one-sided deal.
For each of these (and other) feelings that arise, you merely sort out each feeling and allow it to present itself to you. If the feeling is 'loose' enough (ie not too polarized), then usually a deep breath in until it matches the feeling followed by a breath out with an asian-style bow either from the stomach or hips (also matching wherever the feeling is, and paying attention to the feelings on the way back up as well) will allow you to 'put the burdens down' and let them go. If the feeling 'hooks' successfully and 'deflates' properly, then you can 'drop' it back into the pool of your feelings or 'put it away' for safe keeping. If it does not, then you can try again or try something else if that doesn't work.
For more intense or important feelings this may not be enough, in which case there are a few possibilities. In many cases you might find a mine, which you can only rebury and try to move around. In some cases your feelings may get tangled and you have to release something else first in order to depolarize the part that you currently have. In other cases the feeling may come with other things, like it may include some metaphorical form or it may reveal memories and complaints and other such things, and in those cases it is necessary to sit with the feeling and relax into it until it reveals what it is about. Sometimes feelings require this just to 'thaw out' enough to be released, even though they may not reveal very much specifically.
The Therapeutic Cycle
In general, if I'm working on some emotional issues that I haven't cleared myself, either I'll be doing a lot of acknowledgment (and bowing) or else I'll be stuck and trying to find a way around. Often when working around being 'stuck' leads into a large amount of polarized energy being released, ie anger and other things that sometimes resemble sewage or otherwise feel like pure violence, which provides a starting point for more inquiry and acknowledgment. Sometimes this requires finding someone whose parts will either agree with or polarize with my own or changing modes completely.
Conversely, when I am working with someone whose dominant emotional issues are things I've already worked through (and assuming I'm coherent enough to manage therapy) then I tend to use provocative therapy and hypnotherapy more heavily. Those approaches are comparatively much more rapid and effective if you can find a clear way to apply them in order to expose a person's issues and redirect their behavior. It can also be substantially less painful than trailblazing methods thanks to the emotional support of someone more advanced. The more skilled and emotionally advanced the 'therapist', the less painful and time consuming therapy becomes.
For comparison and informational purposes, currently I am somewhere within the second phase of the Diamond Approach. I have seen brilliance, which looked like a shimmering pool of sunlight (or a lake with no lake) but which did not feel like much of anything, and later on I also saw the partly-completed integration of all of my 'essence'. It was much like Mr. Almaas described in that it was a bit like a glowing jeweled egg with some of the facets shining rather brightly while others were still clouded. At the time I had actually been thinking about 'god', and I've quickly found that 'looking at it' actually hurts because its beauty and purity emphasize the pain and stuckness of the parts which are still clouded. It is perhaps somewhat easier in that I do find that I have more choices at any point as compared to the first phase, however I cannot say that the turmoil or suffering is any less intense, and in some cases it is actually much worse.
You could easily say that my ultimate goal is to be able to look directly at 'god', or equally to be one with all of the things that people truly want in life. Right now, though, it's a very slow (although steady) process of polishing and letting go of everything that I try to keep for myself.