there's no auxiliary verbs in chinese, and you needn't change the sentences' structure when you ues them. just add it where it's needed.
can, want are used as general verbs; must is used as adverb. well, you needn't remember this, what you should know is their chinese meaning:
1.can- neng(/) ; hui(\ )
eg: *I can speak chinese- wo neng shuo zhong wen & wo hui shuo zhong wen.
*Can you speak chinese? - ni neng shuo zhong wen ma? & ni hui shuo zhong wen ma?
2.must- yi ding(/\); bi xu(\-)
eg: *you must have been to china.- ni ken ding qu guo zhong guo. (means ni yi ding qu guo zhong guo.)
*I must leave now.- wo xian zai bi xu zou le.& wo xian zai bi xu li kai le.
3.want-xiang(v); xiang yao(v\)
eg: * I want to eat. - wo xiang chi fan.
* what do you want?- ni xiang yao shen me?
in fact we learn want as phrase "want to do sth", not just want. sometime chinese would say "i think want a book. -wo xiang yao yi ben shu." the reason for the mistake is that "want" means "xiang" & "xiang yao" in chinese'.
can and must is even difficult for those students in china also, so i don't think it's good idea if you learn it by yourself. well, learning is for using. if you don't care about it, just do it! and good luck!