I've thought about writing in my diary since the first day of this year but I didn't even buy a notebook.
So this is my first diary entry on this side (do you mean site, or this year?)
Today was my a school day, everything went along like it always used to does and nothing special happened.
I had two classes, one presentation about psychology and got a lot of homework. At lunch time, my friends and I tried very hard to get the coupon for food, it was very crowded but finally we all had lunch and went to class on time.

Now I'm trying to finish my homework.
Have a good Dream. ^3^ (We don't have this expression in English but I like it :))

Not many corrections really, just small things :)

The first day.  The First Day <<If this is a title then it should be capitalized>>

I've thought about writing diary since the first day of this year but I didn't even buy a notebook., so
So this is my first diary on this side. site
Today was my school day,. eEverything went along like it always used to and nothing special happened.
I had two classes, one presentation about psychology, and I got a lot of homework. At lunch time, my friends and I tried very hard to get the coupon for food. it  It was very crowded, but finally we all had lunch and went to class on time.
Now I'm trying to finish my homework.
Have a good Dream. ^3^