Learn Arabic (Modern Standard): أكتب رسالة على المكتب.

In Arabic, you do not always need to say the standalone pronoun for "I" (أنا) because it is built directly into the verb. The letter أ at the beginning of أكتب tells us that the subject doing the action is "I".

Why is there no Arabic word for "a" before رسالة (letter)?

Arabic does not have an indefinite article like "a" or "an". If a noun does not have the prefix for "the" (ال) attached to it, it is usually understood to be indefinite. Therefore, رسالة on its own simply means "a letter".

The translation says "at the desk", but doesn't على usually mean "on"?

Yes, على literally translates to "on". While in English we say we sit "at" a desk to write, in Arabic it is more natural to say you write "on" the desk (على المكتب). Prepositions often do not translate exactly one-to-one between the two languages.

I noticed أكتب (I write) and المكتب (the desk) look and sound similar. Is there a connection?

Definitely! Most Arabic words are built from three-letter roots. Both of these words share the root letters ك-ت-ب (k-t-b), which relate to the concept of writing. The word المكتب literally translates to "the place of writing", which is why it means "the desk" or "the office".