"I want you to buy that."
Translation:Je veux que vous achetiez ça.
I'm not understanding why "I want you to buy that." can't be translated as "Je te veux acheter cela." I'm trying to wrap my head around the grammar but in English it sounds like this is basically "I want that you buy that." But it's not clear to me why that's necessary/important.
To want someone else to do something requires the subjunctive:
Je veux que tu achetes ça.
Reverso has a nice little guide for how to conjugate every verb in all of it`s forms: http://conjugator.reverso.net/conjugation-french.html