This is not just a diary, but a diary especially for improving my English daily conversation.
So, if there are simpler way of saying things, please teach them to me.
ご質問ありがとうございます。
"This is not just a diary,"＝「これはただの日記ではありません」
"but a diary especially for improving my English daily conversation."＝「私の日常英会話を上達させるための日記です。」
"So, if there are simpler way of saying things,"＝「なので、もしもっとシンプルな言い方がある場合は」
"please teach them to me."＝「それらを私に教えて下さい。」
ご参考に。
アメリカ合衆国 
