Learn Polish: Moja koszula jest biała.

In Polish, describing words must match the gender of the noun. The word for shirt, koszula, is feminine because it ends in -a. Therefore, the word for my changes from its base form mój to the feminine moja, and the color white changes from biały to biała.

Why isn't there a word for 'the' or 'a' before shirt?

Polish doesn't have articles like 'a', 'an', or 'the'. The word koszula on its own can mean shirt, a shirt, or the shirt. Context tells you which one makes sense, but since you are saying moja (my), you don't need any extra words anyway!

Do I have to include the word jest here, or can I just say moja koszula biała?

Yes, you need jest to make it a complete sentence. It is the form of the verb 'to be' meaning 'is' for a single object (he/she/it is). Without it, you would just be saying 'my shirt white', which sounds incomplete in Polish just like it does in English.