Ah, this thread...lol.
Anyway, to the OP - I am someone who needs time to myself to fully process things and understand what my feelings/thoughts are. This is beyond emotions, though, this is related to everything. So, no, I may not know in the moment what I think/feel, but after I reflect on all of it for a while (a few hours, a few days), then I'll know where I'm at. Also, I really do not like having emotional reactions to things because I know that in many cases the emotions are transitory so I see no 'point' in externalizing anything that I don't know for sure yet will be relevant. I have NO desire whatsoever to emote an emotion just because that's what I'm feeling in a given moment, because I KNOW it may be temporary. It may be a moot point 15 minutes later, or the next day, or more to the point, I may have no idea, without the alone-time-reflection, whether or not it is something major or something moot. Or simply my perceptions being screwy for that day (and I therefore don't trust them) because I know I'm in a negative mood to begin with, and my mood is going to taint my ability to see things accurately. Therefore I'm not going to stress/upset the other person if it may be moot or my own deal. Thus I stay quiet, or will simply say I'm not sure what I think/feel and need to think about it.
So sometimes - particularly in more complex interpersonal situations - I don't know what the root cause of my emotion is, or even whether I consider it 'worth it' for all parties for me to mention it; so I need that time to myself to figure out what exactly it is, if anything, and then IF after that reflection I realize I need to talk about it or need to address something with someone else, or change a situation, then I will do so.
Or finally it's simply an emotion that I'm quite familiar with in myself, that has nothing to do with any particular situation, but is just part of my general 'baseline' emotional state and to Jock's point, something I've catalogued and basically know that it'll go away in 10 minutes, or in a day, or whatever. It's nice to have gotten to the point where I have enough 'history' of myself to know the patterns when it comes to my own thought and feelings; therefore I do a lot of self-monitoring/self-checking quite a lot, keeping tabs on myself.
So... direct answer to the OP: How do I deal with my emotions? I analyze them and want to solve for them/figure out why I'm feeling what I'm feeling. That's basically it. My goal is to get out of the negative emotions / understand them such that I can change the situation or my understanding/self. With the positives, I don't have much of a need to analyze them; I like being happy.