Meeting people.

Yesterday I was remembering the first time I met one of my best friends. It was February and the weather was awful outside, the temperature was low and it felt cold. At that time, I was studying at university so I used to go to the College library very often to study. The infrastructure of the library was good and we had a lot of space to study, with big tables and good lighting.
That day, there weren't many free chairs so I chose one and, in front of me, there sat a person who was studying, according to her notes, the same course as me. She was doing exercises for a subject which I had passed the year before, so I decided to help her by explaining to her some concepts about structures.

This was how we starting talking and, until today, we are good friends.

Meeting people.

Yesterday I was remembering the first time I saw one of my best friends. It was February and the weather was awful., Outside, on the street, the temperature was low and it was made cold. To At this time I was studying at university so I used to go to the College library very often to study. The installation layout of the library are was good and we had a lot of space to study, with big tables and good lighting.
That day, there wasn't weren't many free chairs, so I chose one. and, I saw from the notes of the girl sitting in front of me there was a girl, there was sat down a person who was studying, according to her notes, that she had chosen the same career than as me. She was doing exercises about on a subject which I had been passed the year before, so I decided to try and trying to help her by explaining to her some concepts about structures.

This was the way that we starting to talk and we are still , until today, we are good friends.

Meeting people.

Yesterday I was remembering the first time I saw one of my best friends. It was February and the weather was awful, outside, on the street, the temperature was low and made cold. To this time I was studying at university so I used to go to College library very often to study. The installation of library are good and we had a lot of space to study, with big tables and good lighting.
That day, there wasn't many free chairs, so I chose one and, in front of me, there was sat down a person who was studying, according to her notes, the same career than me. She was doing exercises about a subject which I had been passed the year before, so I decided trying to help her explaining to her some concept about structures.

This was the way that we starting to talk and, until today, we are good friends.

Yesterday I remembered the first time I saw one of my best friends. It was February and the weather was awful on the street, it was cold. At the time I was studying at university and I used to go to the library often to study. The library was well insulated with a lot of space to study, big tables, and good lighting.  
That day, there were many few chairs to choose.  I chose one next to a person who was studying and according to her notes, she had the same career as me. She was doing exercises on a subject which I had passed the year before.  I decided to help her by explaining some concepts on structures.

This is how we started to talk and now we are good friends.

Meeting people.

Yesterday I was remembering (thinking about we don't really say "was remembering" for this context. You could also say Yesterday I remembered) the first time I saw one of my best friends. It was February and the weather was awful, outside, on the street, the temperature was low and made cold (In English, we use To Be to describe the weather, also saying the temerature was low and it was cold is repeating the same thing twice basically. Saying It was cold sounds more natural). To At this time I was studying at university so I used to go to the (need an article) College library very often to study. The installation of the library are is good (I don't understand what you mean by this... Are you talking about the heating in the library?) and we had a lot of space to study, with big tables and good lighting.
That day, there wasn't many free chairs, so I chose one and, in front of me, there was sat down (it would be assumed that this person was sitting down so no need to say it. A better way to say this would be: and there, sitting in front of me, was a person...) a person who was studying, according to her notes, the same career than as (you want to compare) me. She was doing exercises about a subject which I had been passed the year before, so I decided trying to try (you already conjugated the first verb so every verb after is in the infinitive) to help her by (use by to show that you are doing the action for her) explaining to her some concept about structures.

This was the way that we starting to talk and, until today (until is very immediate and saying until today makes it sound like you were friends up until today and at this point after today, are no longer friends), we are good friends to this day.

Very good! Some small mistakes, mostly with particles and that kinds of thing.

Keep up the good work