When feeling a really intense emotion, how can I look objectively at myself to see what a normal experience with this emotion should be?

I think if you've been keeping a journal or diary, it would be really helpful to read your older entries when you went through similar experiences in the past. It could give you some perspective of what a normal experience with the intense emotion that you're currently feeling should be. You could also ask your trusted friends or member of your family about it.

Firstly I'll try to identify what issue causes this intense emotion. Usually there will be some extremely judgmental ideas or thoughts in addressing this trigger issue. I'll try to "take away" this judgmental element and try to view the issue from another perspective, or maybe I'll also give some other explanations to the issue. Usually by switching to another perspective, I'll be able to what emotion should I label to this specific issue.

It's very easy to get carried away by an intense emotional experience. One way to prevent this is to lay out the facts for yourself. Think about what triggered your feeling this emotion. Don't just replay the moment or event: state it back to yourself factually, using descriptive rather than emotive and exaggerative words. Keep in mind as you do this that there are automatic thoughts you have in response to a situation, and subsequently there are helpful thoughts that you can prioritise instead, to guide your emotions back to a manageable level.

Try writing it out. Write how you feel, and then let it sit for a couple of hours and then write a response to yourself as though it was someone else that wrote your feelings.

One of my worst words is "normal." It forces someone to think of themselves as "abnormal" or "not right." So let's toss that word out and maybe instead find a constructive way to process the emotion. First things first, take time for you. A reaction to an intense emotion is quick, almost like a shock, and can be painful. Do not react, instead recognize the trigger, the emotion, breathe deeply, take as much time as you need to allow the emotion to process. Then use the coping skills that are considered healthy for you to move forward.

Some people feel more intensely than others, so there isn't really a "normal" experience. Perhaps try to identify the intensity of your other emotions and compare them in relation to the one you are presently experiencing. Sometimes the answer is to consult a professional.

I think about previous experiences when I had thought or felt similarly. If it's a new situation, I work to calm myself down as much as possible when having that emotion before continuing.

Why do you think the emotion you feel is intense maybe it's normal for you the level of emotion varies with each

I think you have to live it, take deep breaths and try to calm yourself. Like you wrote, when you are living a intense emotion, it's hard to keep your mind clear and make good choices. A normal experience with this emotion is relative. There is no normal, bad or good reaction. I think it's just something you have to live and learn how to cope with it :)

This answer might seem contradictory to what you are trying to achieve, however, emotions are supposed to flow naturally, so, that intense emotion will have to fade away before you can look at the situation objectively, be patient, breathe, and just let go, do not overthink it, this way you will learn about yourself, and eventually emotions will sort of flow faster and/or lose power over your reactions, letting you experience life in a calmer way.