I was wondering how to use the DNA splicers.
Yup.It works only for both of them only if they have the same ID.Kyurem can be fused with either zekrom or reshiram.Zekrom and reshiram cant be fused.
That is what they do, fuse Kyurem with Reshiram/Zekrom.
You need either Reshiram or Zekrom to use it yes.
If you have the DNA splicers you can fuse kyurem with reshiram/zekrom in other words, yes
You must have both Kyurem and a Zekrom / Reshiram in your party. You can use them on Kyurem without the two Pokemon, but when you try to select a Pokemon to fuse it with, it will fail.
You must fuse reshiram/zekrom with kyurem. Not reshiram wit hzekrom.
reshiram: White Kyurem
zekrom: Black Kyurem