There are two different forms of the problem of evil: the logical problem of evil and the existential problem of evil. They're very different objections and require different responses.
The logical problem of evil claims that there is a logical contradiction between an all-powerful God and the existence of evil. This challenge is considered solved by many philosophers and theologians. Brett wrote about it here. You can find a good summary here. And an answer by Greg here.
The existential problem of evil is more of a grievance or complaint that God allows evil. It asks why a loving God would allow evil. It doesn't find anything illogical about evil and God. It asks for a reason. This objection isn't formed as a logical syllogism, as the logical problem is, so the answer doesn't find fault in the deductive reasoning. The answer to the existential problem of evil shows why God could have a sufficient reason to let evil exist, explaining why a loving, good God would allow evil. Another way to answer is to undercut the grounds for the complaint. Greg discusses that here.
So make sure you understand the nature of the objection before answering. There are good answers for either one, you just want to make sure you answer the question being asked.