Not bad for a first note.... However, can I make a few suggestions? The corrections are in red.

First note

Hi. This is my first note.
I accidentally visit this site when finding way to learn English.

I visited this site on accident trying to find ways to learn English.

or

I stumbled onto this site trying to find other ways of learning English. 

I want to learn how to speak and write English better.

I think I can read and hear English but I am bad at writing and speaking.

My English is limited. I can read and understand English, but I am not so good at writing and speaking the language.

So I come itaki everyday free time.

On my spare time I come to itaki every day for that purpose.

I am bad teacher Korean, but you want some help, please contact me. 

Um. This is my first note, and i am better next.:)

I also teach Korean. I am not the best at it but if you want some help feel free to contact me.

This is my first note and the next one will be a lot better.