Questions & Answers about اليوم أنا مشغول في العمل، وصديقتي مشغولة في الجامعة.
In Modern Standard Arabic, the verb to be is usually not stated in the present tense.
So: أنا مشغول literally looks like I busy, but it means I am busy.
The same happens in: صديقتي مشغولة = My friend is busy
Arabic does use forms of to be in the past and future, but in the present, a nominal sentence like this normally just puts the subject and the predicate next to each other.
اليوم means today, and here it functions as a time expression.
Putting it at the beginning gives a slight emphasis to today, as in: Today, I’m busy at work...
You could also place it later, for example: أنا مشغول في العمل اليوم This is also natural, but the emphasis is slightly different.
Here أنا is the subject of the first clause, so it is important.
In a sentence like أنا مشغول, the adjective مشغول by itself does not tell you who is busy. Arabic needs something to show the subject, and here that is أنا.
In conversation, Arabic sometimes drops things that are understood from context, but in clear, standard written Arabic, أنا is the normal and safe choice here.