I'm exhausted...

October 14th
The sky was clear.

I was busy with work. There were a lot of things to do today but we were only three in all there was only three of us !
I think we will be busy again tomorrow... However, I will go for a drink with a friend after work. Therefore, I think I can do my best at work again tomorrow!

I agree with Ryan. This note is good and your use of "However" and "Therefore" are grammatically correct but they are not commonly used in such an casual message. Also, your use of ( ... ) is used in casual communication and it is fine use ( ... ) to show you are thinking about what to say next but it would not be used for a more formal note. I will write the letter how a native speaker would do it. If you have any questions or comments about the changes I made to the note just ask.

I was really busy at work today. There was so much to do but there was only three of us working ! I think it will be just as busy tomorrow so I am going out for a drink with a friend after work. Having fun tonight will help me be ready to do my best at work tomorrow !

Next week I will be looking for a person who wants to practice Japanese with me in exchange for help learning English using Skype. I have only been learning Japanese for one month. Maybe we can help each other. Let me know if you are interested.

I'm exhausted...

October 14th
The sky was clear.

I was busy with work. There were a lot of things to do today, but we were only three in all!
I think we will be busy again tomorrow... However, I will go for a drink with a friend after work. Therefore, I think I can do my best at work again tomorrow!

There are no major grammatical problems with your post. Congratulations! I just added some extra commas where they fit nicely.

Let's talk about writing style instead. Some of your style is casual ("I'm", "a lot", "...", "go for a drink"), while other parts are more formal-sounding ("However", "Therefore", and using "we will" and "I will" instead of "we'll" and "I'll").  It sounds best to keep your style consistent throughout, so keep that in mind.

Anyway, good work overall!