Dave,
Tami's right: you do want the Brummel splace:
http://www.neropes.com/SPL_12Strand_EyeSpliceBrummel.aspx. The instructions are as clear as one could hope. Note that the resulting eye is secure even without the buried tail, but you should still bury and stitch for full strength.
You really don't need a splicing wand for easy single-braids like vectran, though I do covet the small Brion Toss splicing wand. The wands were available through West Marine for a while, or on his website. I never got one because of the price, and I already had a complete set of Samson fids and a pusher, but I'd recommend the wand over conventional fids any day.
Tami's also right that the Brion Toss splicing video is awesome. I don't recall it covering the single-braid splicing (at least not the version I saw) but it is awesome, covers double-braid splicing, creating a continuous loop, splicing laid rope, arborists (super tight braid) rope. The man is a splicing machine!
--Glenn