All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
First of all, it should be mentioned that a Muslim should not initiate a debate with non-Muslims and try to convince them with the truth unless he is grounded in Islamic knowledge which will allow him to convince his opponent and ward off his misconception, otherwise the debate will be an affliction for the people who are upon falsehood and it would weaken the position of people of the truth. Moreover, this may even shake the faith of the Muslim who is debating them, so one has to be very cautious about it. As regards the actions of non-Muslims, Allaah clarified to us in many verses that their actions are void. Allaah Says (which means): {And what prevents their contributions from being accepted from them but that they have disbelieved in Allaah and in His Messenger.}[Quran 9:54]. Allaah further Says (which means): {And whoever denies the faith — his work has become worthless, and in the Hereafter, he will be among the losers.}[Quran 5:5]. Allaah also Says (which means): {And We will approach [i.e. regard] what they have done of deeds and make them as dust dispersed.}[Quran 25:23]. In another verse, Allaah Says (which means): {As for those who disbelieve, their deeds are like a mirage in a desert. The thirsty one thinks it to be water, until he comes up to it, he finds it nothing but finds Allaah before him, and He will pay him in full his due; and Allah is swift in account.}[Quran 24:39]. Another verse reads: {The example of those who disbelieve in their Lord is [that] their deeds are like ashes which the wind blows forcefully on a stormy day; they are unable [to keep] from what they earned a [single] thing.}[Quran 14:18].
All the above are evidences from the Quran, and it is Allaah Who accepts the deeds and it is He Who gives a recompense for them. So, it would be very strange for a person to disbelieve in Allaah and associate with Him others in worship, for which He had sent no authority, and then expect from Him the best recompense.
Therefore, the deeds of a non-Muslim are not accepted from him by Allaah on the Day of Judgement, but Allaah does not wrong anyone. The non-Muslim will be rewarded for his good deeds. The Prophet said: "Allaah does not deal unjustly with a believer about a good deed as he is given blessings for it in this world and is rewarded for it in the Hereafter; but the disbeliever is given in this life the reward for good deeds he has performed, and when he comes to the Hereafter, there is no good deed for which he can be rewarded." [Muslim]
What a non-Muslim should do is embrace Islam, the true religion which is the religion of all the Prophets and Messengers. Allaah Says (which means): {So believe in Allaah and His Messengers. And if you believe and fear Allaah, then for you there is a great reward.}[Quran 3:179]. Allaah further Says (which means): {O mankind! Verily, there has come to you the Messenger (Muhammad ) with the truth from your Lord, so believe in him, it is better for you. But if you disbelieve, then certainly to Allaah belongs all that is in the heavens and the earth. And Allaah is Ever All-Knowing, AllWise.}[Quran 4:170].
As regards how to explain the truth to non-Muslims and call them to Islam, then this requires a person to have knowledge and it is not up to everyone to do it. One has to clarify to them the perfect proof and argument [evidence], and point out to the discrepancies and contradictions that their books contain, and so forth.
For more benefit, please refer to Fataawa 84349 and 89122.
Allaah Knows best.