First of all, it's "저는 학교에 가고 싶습니다."

원하다 sounds formal. Koreans say "싶습니다." a lot more.

If your textbook doesn't have "싶습니다." then it's not a good book.

"To want" has 2 differen usages in Korean language.

I mean the meaning is same but the usages are different.

I think that's why you got confused :)

1. Verb/Adjective+고 싶다

나는 학교에 가고 싶다(Basic) - I want to go to the school.

저는 학교에 가고 싶습니다(Polite) - I want to go to the school.

나는 샌드위치를 먹고 싶다 - I want to eat a sandwich.

2. Noun+을/를 원하다

나는 돈을 원한다(Basic) - I want the money

저는 돈을 원합니다(Polite) - I want the money

그녀는 남편을 원한다 - She wants a husband

그는 새 자동차를 원한다 - He wants a new car

So +다 is the Basic form and +입니다/습니다 is the Polite tone.

And "to want" has 2 different usages in Korean langugae.

I hope my explanation will be helpful to you :)

The above answerer is completely correct. I will add a little.

싶습니다 comes from the verb 싶다.

싶다 -> 싶 -> 싶+습니다 -> 싶습니다

This is an extremely common word. Which book are you using?