I like that book.
In the DP theory, the determinative "that" is head and the noun is the dependent. The demonstrative determinative "that" is just as much a determiner here as "the" is, so there is no structural difference between the book and that book; they are both NPs.
There are a couple of facts to support the NP analysis. ...
First, a note: this isn't the only possible way to answer the question. You can also argue for it being an NP with special restrictions that mean it can only combine with the null determiner. There are also some theories which don't use DPs at all, just different flavors of NPs with different restrictions. But to me, that adds extra complexity and headaches ...
Good question. Constituency is the theory behind such a tree diagram. There are a bunch of different Constituency tests which you can do on paper:
[ [John] [ [hit] [ [ [the] ] [ball] ] ] ]
[John]: Who hit the ball?
[the]: John hit which ball?
Wh-substitution and do-support-substitution:
[hit]: John did what to the ball?