A good book on the Reformed view vis-a-vis an Arminian is James White's,
The Potter's Freedom
where he interacts with Norman Geisler's,
Chosen But Free. I don't really recommend Giesler's work unless you want to see the Arminian view presented at length, as White fairly quotes NG in his own book.
There are key verses (1 Tim 2:4; 2 Pet 3:9, etc) misapplied by Arminians one should know how to explicate properly, in order to interact with them in an edifying manner. Also the use of the phrases or words such as "all men", "the world" etc needs to be understood as they are often misapplied. As someone noted above, it is good to study the exegeses of scholarly Arminians and their rebuttal by Reformed saints to get a good grasp of the arguments that may be used. John Owen's book,
The Death of Death in the Death of Christ, and John Gill's,
The Cause of God and Truth are both good resources for Reformed exegesis of these things.
As Rich (and others) pointed out, it is always good to keep in mind that the person we are talking with may have more pressing and crucial needs than the doctrines we might like them to appreciate. A stable, intimate relationship with the Lord Jesus comes to mind as likely the foremost. Reformed souls have a great advantage there as the doctrines of grace naturally tend to engender just this. It is what He has done for us -- and is to us -- that take priority over what we should do for Him. Many folks are on a religious performance treadmill, and they have no rest, and no assurance of His acceptance or love. As Rich said, one may open these joyous revelations in God's word to them without using the "Reformed buzzwords" that may turn them off, seeing as we have often gotten a bad press which lingers in many minds. I include even the Bible version issue: there are matters that come before that as well.
Do we love these erring believers, or just want to have them conform to orthodoxy? Without love there is no genuine edification (1 Cor 8:1).