The following strategy is easiest to pull off with two of the dragons present in the game (they're both in Shadows of Amn). It could work with the other dragons, but it would be much more difficult to do. It requires that you have a Priest who has the Magic Resistance (5th level) and Harm (6th level) spells. A very easy way to kill Firkragg (red dragon) and Thaxll'ssillyia (shadow dragon) is to lower the dragon's magic resistance with the Magic Resistance spell, bring his HP down to 1 with the Harm spell and then finish him off with anything that can hit him (Magic Missle works well for this). Dragons have a very high magic resistance, and if you use the Magic Resistance spell on one, its magic resistance will be lowered to a much lower value. Once the resistance has been lowered, you will have a much better chance of getting a successfull Harm hit. The other key aspect of this strategy is that you need to make it so the dragon is not hostile when you're trying to do this. Firkragg will not be hostile if you choose the appropriate responses in your conversation with him, and if you have the Shadow Dragon Wardstone in your inventory when you go into his room, Thaxll'ssillyia will not be hostile either. While the dragon is not hostile, cast Magic Resistance on him (he won't attack you if you do this), cast Harm and then save your game. Attack the dragon and hope that your Priest scores a successfull hit. If he or she does, simply go in for the kill. If he or she misses, reload your saved game so you can try again. This could take many reloads to pull off. Most likely you will need to pull off a critical hit to hurt the dragon; critical hits ignore Armor Class.

There's always fake-talking them, if the dragon's not hostile (as can be done with Firkraag, the dragon in the Temple of Amaunator with the unpronounceable name, and Adalon - don't remember if the black dragon in Suldanessellar starts friendly or not). Fake-talking is cheap, but works. How to fake-talk - pause and select your entire party. Have them "talk" to the non-hostile dragon, then "attack" it. Unpause. Let it run for a couple seconds as you and your friends attack the enemy (it's still not hostile). Pause. Talk. Attack. Unpause. Let it run for a couple seconds (you can't let the dragon talk to you or go hostile, or it's all over and you've got to finish it normally). Pause. Rinse. Repeat. Kill dragon. Loot. This also works on Demogorgon in ToB. Various strategy guides say that fake-talk was fixed, but it's not.