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?