I think that learning to feel emotions can be a different process for everyone.
First I think it begins with acceptance. Think about it, your TMS began in it's earliest form because of some sort of internal conflict - in general it's about who we truly are and how the "world" sees us (or how we interpret how the world sees us). Acceptance is multi-level, and it is an evolving process - we are who we are. We are OK being happy, being angry, being sad - accepting that we are not perfect, and that we ARE loved and valued by people and also intrinsically by the universe (or God, however you see this great power). It's by accepting that you are not your thoughts. Your thoughts are your brain, but you are not your brain (even tho it often wants us to think it is) - your human essence like all sentient beings goes far beyond your simply being a brain or occupying space on this planet. It is that flicker of life within you. Neither good no bad - it just is. This is a big concept but I think it resonates with many people who meditate. You just accept who you are, who you have become and lessen the internal fight over things like: being told you are a perfectionist but you think that is "bad" for you, or being angry at things you have been taught you should not be angry at. Learning it's OK.
The other thing is tolerance. You did not tolerate the breadth of emotions, and eventually created pain to feel SOMETHING. Some people feel some emotions, others feel none. You become aware that you don't feel emotions "somehow"...however you kind of do. You probably feel emotions of some kind as "symptoms" - you get embarrassed and your face gets hot and your stomach does a flip flop. You get angry and you want to clench up - like clench your hands, you might get a little sweaty.... I think this is why somatic tracking is taught. So that we can become tolerant to any sensations, and so that eventually emotions aren't so scary and overwhelming (somatic tracking isn't for everyone). You have to become tolerant to being uncomfortable with sensations and thoughts (Sarno says to get back to activity as a way to start that desensitization or to increase tolerance). This doesn't have to be perfect. The idea is that SOME of the time you are aware and or feeling the bredth of your emotions and that reduces stress and hence suffering.
The key as
@Booble points out is awareness. Teaching yourself to stop and become aware of your emotions over and over and over again until it becomes habit. This can take days, months, years - however long it takes. It's not a perfect process and you won't do it 100% of the time. You learn to do it enough that it reduces your stress and suffering.
There are some folks that you can simply explain this process to and they just go "oh" and are able to do it. Then others like myself who this is a very long process. I had 50+ years of NOT doing any of these things, and many personality traits and thoughts that were inaccurate that must be re-learned. It takes time. Over this time, I've learned to have more "fun" with the process and experiment. I've also learned to look for clues in things others people say.
I saw an interview with the TMSwiki founder, Forrest where he mentions he really has never much felt his feelings (or certain feelings) and he rarely has physical symptoms that become chronic anymore. He has lessened his fear of any symptom and sees them for what they are, he accepts how his internal operating system works and doesn't strive for things like 100% feeling feelings. This is working for him, probably because he isn't struggling internally with it all.
I've heard this termed as learning to "get out of your own way".