Letter
noun, の adjective
A hand paper is a letter because letters are generally written by hand on paper. If you want a more graphic image, imagine writing a letter on your hand, and how much it would hurt to chop off your hand and send it.
てがみ
The reading is double kun'yomi. Think of 手紙 as two words mashed together — a letter is a thing you write by hand (て) on paper (かみ). You've learned those readings already, so you should be able to read this! Just watch out for the rendaku on がみ.
それは、父からの手紙です。
It is a letter from my father.
切手が足りなかったのか、学校からの手紙が中々来ません。
Perhaps, it didn't have enough stamps. A letter from the school still hasn't arrived.
外国への手紙の出し方を教えてくれませんか？
Can you teach me how to mail out a letter to a foreign country?