I did not register during registration period due to financial problem and I need to register before I can write exams. The only options is to write a letter to the registrar. How do I write it?

You don't say what country, what school, etc., so we can only guess.
You don't even say if you have the money now.
Assuming you do, you find out the name of the registrar and address that person by name.
Dear [Mr. Mrs. Ms. Registrar],
I would like very much to be able to register at this time, and sincerely regret that I wasn't able to at the required time. Attached are copies of papers showing my financial situation then and now.
Any consideration you can provide will be gratefully appreciated, and if there is any more information you need, I will send it immediately.
Sincerely,
me

Don't count on that working, however, if the school has strict deadlines. Plus, not having the money is a poor excuse for not going to see the registrar during registration to discuss the situation. You just let it slide.