Learn English – “How is going” or “How is it going” or both

As Tyler James Young says in his comment, it would be more common to ask, "How did you get here?" rather than come, and starting your response with the rhetorical question "How'd I get here?" is perfectly natural in casual conversation.

If you were talking about a position/status in life, you'd say something like, "How did I come to be the vice president at the age of 28?" and I think "How'd" would work in informal conversation. If you were talking about a place where you reside (rather than a restaurant or a party, where you recently arrived), you'd also use come to as in "How did I come to live here?"

Since the question is rhetorical (I think that's the proper term, since it's a device rather than an actual question for your listener), "How did" sounds like it's the best overall answer. The dynamics of starting your answer to a question with a question feels more comfortable with a longer answer.

The short answer: Your given change to on which is fine here. Using when would work, but not quite as well.

Further discussion: Disclaimer: This discussion is largely philosophical. Anyone presenting a more clear-cut answer will get my upvote right away.

The reason for these uses deals with our concept of time. when, on, and where are all used to describe time, while an outside observer must question why anything other than "when" is used.

Time is a very abstract concept. You can't see time. You can't put something physical onto time. You can't define a location for time. And yet we try to take this abstract concept and understand it better by comparing it to concrete actions that we can do.

ON:

Even though we can't stand on top of time, we still might say

The man arrived on time at 10:00.

When we read this, we imagine time as a single, discrete thing. It is the best way to take such an abstract concept and make it useful. The man is on a single, brief section of time exactly at 10:00. In this situation, it is easiest to understand time as a thing, so we talk about it in this way.

WHERE:

Lets look at your example in a simple form.

The day where nothing happens.

In this situation, it suits our purposes to redefine our understanding of time to fit the situation. There is no place called time, and yet we make such a place in our head. We imagine a place where nothing is occurring, and use that as a reference. I might imagine a quiet room, and better understand the abstraction of time by using the concrete knowledge of a quiet room to form my understanding of time.

WHEN:

It is hard to form a concept of when because time is infinite in both directions. We have to frame our reference to encompass a beginning and ending point. Infinite time is too hard a concept truly comprehend. For this reason, when is commonly used to cut this infinite concept into a "section" that is easier to comprehend.

When he left, it was over.

We see when and imagine time like a cut piece of rope. The rope might go on a long ways in either direction from the cut, but that is too much rope to deal with. Much easier to picture one section as a reference. This "cut" section of time starts when the man begins to leave, and ends when he is finished leaving. Unlike the other examples, it is difficult to picture time as a thing(on) or a place(where) in this situation, so when is preferred.