An excerpt from Rabbi Kaplan's Handbook of Jewish Thought:
Belief in God and our religious fundamentals is our most precious possession and must be guarded accordingly. The Bible recognizes the atheist and calls him a fool, as it is written, "The fool says in his heart, there is no God" (Psalms 14:1).
We are therefore commanded not to let atheistic thoughts or material desires undermine our faith, as the Torah declares, "Do not stray after your heart or after your eyes" (Numbers 15:39).
This is a negative commandment, depending upon thought, and can be observed at any time by asserting one's will and refusing to be led astray from our faith...
One should be familiar enough with the basics of our religion and its rational arguments in order to know how to answer the nonbeliever. However, religious debates can undermine one's faith and should generally be avoided, as scripture warns, "Do not answer a fool according to his folly, lest you become like him yourself" (Proverbs 26:4).
One should therefore only engage in a religious debate when it is initiated by the nonbeliever and there is danger that he might influence others, and even in such a case one should not debate unless he is thoroughly familiar with the question and skillful in debate. If one has confidence that he can prevail, he may debate, as we are taught, "Answer a fool according to his folly, lest he be wise in his own eyes" (Proverbs 26:5).
The above only applies to a non-Jewish atheist. However, one should avoid debate with a Jewish nonbeliever entirely, even in the above case, since experience has shown that a Jewish nonbeliever is likely to be more intolerant of a faithful Jew than his non-Jewish counterpart. Worst of all are those who were once religious and have left the path of true belief. Any argument with them is only likely to strengthen their disbelief, as we are taught, "Whoever comes to her (atheism) will not return; he will never attain the paths of life" (Proverbs 2:19).