I think you can translate “faire” by “manage”.

Vous souvenez-vous comment moi j’ai fait pour apprendre* le mot passementerie
Do you remember how did I manage to learn the word “passementerie” ?

It makes an emphasis on the manner you did it. It implies it is something not common, but you found a way to do it.

It is very common. You may often use it when someone solves a problem:

Comment t’as fait pour finir aussi vite ?? (familiar)

« Comment [j’ai/t’as/il a/…] fait » is not formal, it is used on common language (a little familiar maybe, but not that much)

“Vous souvenez-vous comment moi j’ai fait pour apprendre* le mot passementerie”
translates:
“Do you remember how I managed to learn the word passementerie”

“mais même si… comment peuvent-t-il faire pour apprendre leur sense ?”
translates:
“Even if… how can they manage to learn their meaning?”

So yeah, “How to manage to” could be a quite accurate translation for “Comment faire pour”

Think about “Comment faire pour” this way: What are the actions it takes to obtain the desired result?

A sentence such as:

Comment j’ai fait pour apprendre le mot « passementerie » ?

is about the actions you took. If you ask instead:

Comment j’ai appris le mot « passementerie » ?

the question is much broader. Answering “from whom” or “where” you learned it would be sufficient.

You can substitute also "arriver à" for "faire pour": "….comment moi, je suis arrivé à apprendre le sens…" I came to learn the meaning… This construction may make it more obvious that a goal is being sought after and then achieved