I like English very much and work [1] to use English every day.

Especially I would especially like to improve my English speaking skills of English.

[1] Perhaps you mean "want"? (~たい) -> "I want to use English every day". Or maybe "use English at my workplace every day"? (...職場で英語で話します)

First notebook entry: Introducing myself

I like English very much and work try to use English every day daily.

Especially I'd like to improve speaking skill of English.(this can be written in 2 ways 
first: I'd like to improve in english 
second: I'd like to improve my communication skills in english) 

First notebook entry: Introducing myself

I like English very much and work to use English every day.

もし「英語が好きで、毎日英語を使うように心がけています」と言いたかったら、”I like English very much and I try to use it every day."がいいでしょう。

「毎日仕事で英語を使います」なら、"I use English every day at work"ですね。

少しでもお役に立てれば幸いです。