I have really put this together for myself, to keep myself grounded in dealing with certain individuals from a certain cultic group. It can be very painful, frustrating, even angering to deal with folks who are blinded and in a cult like this. I hope the following thoughts might help someone else out there in a similar situation:
1. Don't rely upon your own strength. Present facts, think about how they might reply, try to be convincing, but limit or tension that with the fact that the power to persuade is out of your hands. You can't do it. God must.
2. Realize that they are blinded. They don't see glory (2 Cor 4). The battle you are on is a spiritual battle, and God must win it to release them from captivity.
3. God is sovereign. We shouldn't presume upon what His sovereign plan is, but He is sovereign over all of it. We are just called to give a defense and leave the rest to Him.
4. Be prayerful. This relates to #1. God must do it. God must supply words, truth, and wisdom to even present the truth faithfully, much less convince them of it. Trust God, seek His face in prayer.
5. Don't fall into the trap of feeling like you are the sole representative of Christianity, and if you don't "win," then it will just show that Christians can't defend what they believe. You aren't meant to carry that kind of burden, and you can't. Many of these cults have been around for a while, and they are "professionals" at coming up with stuff to stump people. You won't be able to answer everything, and you can take your whole life trying to. You don't have to answer everything, though.
6. Don't let their unwillingness to be convinced make you think what you have to say or what you believe isn't convincing. It can be a nasty trap of discouragement. You start thinking that, unless you are able to answer every single tiny detail and get them to admit it, then you don't have anything convincing at all.
7. Likewise, don't let their constant responses against it make you think that what you believe or are presenting is uncertain. Did you really expect that they would just say, "oh, you are right?" No, they will respond against it, and they will continue to, unless God opens their eyes. This doesn't necessarily mean that what you believe is uncertain. It may just mean that they are unwilling to accept it, which is what we already know. The fallen mind will always make rationalizations to convince itself it is right in rejecting and suppressing the truth, until God Himself shows up and is revealed to them.
8. Don't always allow yourself to fall back into a defensive position. It is very easy to find yourself in one. Suddenly, you are receiving dozens of questions and responses. There is just too much information, too many issues, and you feel totally overwhelmed. Let them give an apologetic for their beliefs. Ask good questions. Let them explain themselves. Let them answer. They have a burden of proof, too. Don't assume it is always your job to fully disprove their doctrines, and if you can't disprove them then they are ok. No, they bear the burden of proof, too. Let them prove them.
9. Ask good questions! Relating to #8, often we find ourselves in the defensive position because we are doing all the talking. When you make an assertion, you have the burden of proof. The more assertions you make, the more "proving" you need to do. Suddenly, the you are under the microscope. We all know, however, that unbelief is not the absence of belief. It is belief in something else. Asking good questions exposes their underlying beliefs for what they are often far better than making a series of statements. Asking good questions also allows you to steer the conversation.
10. Realize that there is a point where you should probably "shake the dust off your feet" and move on. When is that, exactly? I don't think there is a hard and fast rule, but I do think there is a point when you must just say, "Hey, listen. I have shown you many things, but it is obvious that you aren't really interested in examining evidence. You already have your mind made up."
11. Consider how you can demonstrate to them that they do already have their mind made up. This may or may not be useful. Are they using different standards when looking at what you present? Are they blindly accepting things from their cult organization, believing they are being "true Bereans," but then being highly skeptical of anything that tries to disprove what they are taught? Can you demonstrate it to them?
12. Fix your mind upon the LORD, always. Isa 26:3
13. Make your goal to glorify God. Point out false teaching and declare His truth, but have your ultimate goal be to glorify God, not to "win."
14. Be broken-hearted. I almost forgot this one. It is something to be sorrowful for when someone is blind. Though they are responsible, they are still captives -just as you once were.