There are several options Asta. You could use a File control to store a text diary, or use the TinyDB if you want the diary to store locally on your phone/tablet. There are also options to store the diary in the Cloud using Fusion Tables or a Google Spreadsheet.
To help you decide, here are some 'diary' examples posted on the MIT Gallery that should give you some ideas about how you would like to build your diary.

Here are some resources to help you learn to use the AI2 tools A very good way to learn App Inventor is to read the free Inventor's Manual here in the AI2 free online eBook
http://www.appinventor.org/book2 ... the links are at the bottom of the Web page. The book 'teaches' users how to program with AI2 blocks.
To get specific advice, you need to decide how you want to store your diary; in the device or in the Cloud and what tools to use. We you know, ask again telling us exactly what you want to do and what you tried and you will get help.
Regards,
Steve