What are the steps a person from another Christian denomination has to take in order to be accepted into the Catholic Church?

If the person has not been validly baptized, that needs to happen.
If the person has been validly baptized but not validly confirmed, that needs to happen, almost always preceded by confession and absolution.
If the person has been validly baptized and validly confirmed, he needs to make a formal profession of Catholic faith.

Depending on the person's background, he may need to go through a series of preparatory classes or meetings with instructors (priests, other teachers) to be sure he is adequately prepared for the responsibilities he will accept.

Thank you for your answer. Gotta be honest: it sounds quite complicated.

Not really. A person has to receive the sacraments of initiation, and he or she must be ready to do so, insofar as a person is able.

The priest (or, more likely, the DRE) keeps track of the process; all you really need to worry about is fulfilling the steps in the process as you’re advised to take them. When I was undergoing the conversion process (AKA RCIA), the hardest part for me was the waiting (under normal circumstances in the US, the process takes 9-12 months). Of course, your mileage may vary.

RCIA is not universally used, and really shouldn't be in the case of a baptized person (even though it often is).

Since nobody would ever jump into marriage suddenly or quickly, neither should anyone convert suddenly or quickly. RCIA, or an equivalent, gives a person an opportunity to explore and be sure it's what you want.

Thank you. One size does not fit all. Going through Alpha before being allowed into RCIA, mandatory in my parish, just about killed it for me.

Why not? If it was someone I'd like and she was a Christian, I'd marry her today.

The person you marry is your partner for life, the mother of your children and someone you're ready to live and die for. The choice of this person shouldn't be made lightly. Many a tear has been shed by people who married too hastily.

I'm assuming from your profile that you're Eastern Orthodox? I think Orthodox being received into the Church is much simpler than it would be for someone who is not baptized, or who is a baptized Protestant.

to noncatholics, a lot of catholic stuff sounds complicated or whatever..

and even though I have had a lot of problems in the Church (cradle Catholic) I am so thankful I am Catholic and raised that way -- because I have a rather rebellious streak as probably all humans do and if hadn't been taught Catholicism early, probably would have grown up antiCatholic or something. And I would have been the loser (whether i fully realized it or not)

This is true since we acknowledge the validity of all Eastern Orthodox sacraments, you would probably just need to make a formal profession of the faith. I recommend talking to a local Catholic priest to whom you have access if that's possible. If you are in an area where there are Eastern Catholic Churches (as opposed to just Latin Rite Catholic Churches), this will probably be even more straightforward, because you will be a little more familiar with the liturgy.

Why is that so, my friend?

The Orthodox have valid Sacraments of initiation

A couple of reasons, one, the Orthodox have valid Sacraments; and two, there is not a wide gulf between the teachings of the Orthodox Churches and those of the Catholic Church.