I understood most of what you wrote , but here is how i would say it :). glad you had a great first day when you started university.

My first day at  university

I will tell you about my first day at (- the) university. It was August 31, 2009.
It was a bright and sunny day .I woke up very early and it took me a long time to decide/choose what  to wear . ( Optional, but i think this makes it clearer that these things in your day , were a sequence of events in your day )~Before i left, my new neighbors said to me ( you do not need a : here. Any time you write a quote, just use " . However, if you were writing a play , you would write the charector's name and then write : to show what they said.   "Good luck!"
When I came out of my ( the isn't wrong, but it sounds better to say "my" here)dorm, I thought about my new teachers and friends.
I met my new friends near another dorm . did you meet them near your dorm or another dorm ?There were two girls, who were in my class.( I think you mean that you and your friends were going to the railway station ? All the way to the railway station, me and my new friends talked about/ discussed  our anticipation of the Moscow State University.  
By the way ,my first lesson was High Mathematics, which was taught by a very old professor. He had blue eyes and he was kind towards us/ he showed us a lot of kindness towards us or to us because it was it  our /the first lesson ever at the university .i might say "Dispite this " Because i think you mean, even though your teacher was kind and you had a good lesson, you have more a preference  or you are better are social and liberal arts? are you only doing maths, regretting what that chose maths? or are you studying a few subjects but there are some which you prefer?Are you More of a creative person than a logical person so you think a subject like  maths would be harder for you?  this was abit unclear . Maybe you would like to say I am more of a creative person , therefore I thought I would have 

A harder time understanding maths.

I can't remember how the day ended  ,but I thought it was excellent!


What do you think about my pronunciation?

First day at the university

I will tell you about my first day at (the) university.(you could say: let me tell you about my first day) It was August 31, 2009. (you pronunciated august thirthy one.. but the correct is august third first)
It was a sunshine and a brightly day! I woke up very early and I hadn't chosen what I dressed for a long time. My new neighbors said to me: "Good luck!"
When I came out of the dorm, I thought about new teachers and friends.
By the way, I met my new friends nearby a dorm! There were 2 girls, who were in my classroom. All the way we said talked about our anticipation of education in the Moscow State University of Railway Station.
By the point my first class was High Mathematics, which was taught by a very old professor. He had blue eyes and he was kind in to us, because there it was his first lesson after school. But I prefer social and liberal arts, therefore I understand that I will have some problems with this subject.
Actually I don't remember how was the end of this day, but I think that it was excellent!


What do you think about my pronunciation?


The verb say needs a preposition to.. my neighbours said to me.. 
and be careful.. if you  use tell.. my neighbours told me ( no preposition) 
the pronunciation is good

First day at the university

I will tell you about my first day at the university. It was August 31, 2009.
It was a bright and sunshiny day! I woke up very early and I took a long time choosing what to dress in. My new neighbors said to me: "Good luck!"
When I came out of the dorm, I thought about new teachers and friends.
By the way, I met my new friends at a  nearby a dorm! There were 2 girls, who were in my classroom. All the way on the road we talked about our anticipation of education in the Moscow State University of Railway Station.
By the point, my first lesson was High Mathematics, which was taught by a very old professor. He had blue eyes and he was kind to us, because there was a first lesson after school. But I prefer social and liberal arts, therefore I understood that I will have some problems with this subject.
Actually, I don't remember how was this day finished, but I think that it was excellent!


What do you think about my pronunciation?

[Your pronunciation is good.  I could understand what you said, and that's the most important thing.]