How to prove a problem is NOT NP-Complete?
A problem $Q$ is NP-complete if it is both NP-hard and in NP.  This means that you need to disprove one of these two.


Under the assumption that P $\neq$ NP, you can give a polynomial time algorithm solving $Q$.  Rarer, under the assumption that graph isomorphism is not NP-hard, you can show that $Q$ is polytime reducible to graph isomorphism.
You show that $Q$ is not in NP.  This is harder, and you must usually use other assumptions, like non-collapse of polynomial hierarchy, that NP $\neq$ coNP or show that it is hard for some other class higher than NP, e.g. by showing that it is NEXPTIME-hard.


Usually, the answer is to give a polynomial time algorithm, which would be the simplest for DNF-SAT, but this relies on the hypothesis that P $\neq$ NP.  However, proving that DNF-SAT is not NP-complete without any assumptions implies, as Shaull points out, proving that P $\neq$ NP, so that is somewhat trickier.