Unlike modern knitting naalbinding requires only a single needle. Typically between 2.5 and 5.5 inches, though other sizes are used and many people simply use commonly available, blunt tapestry needles.
This Instructable shows how I made one of bone, similar to a number of examples from archeological sites from Northern Europe and Scandinavia. Mine is definitely on the small side. Though, I haven't developed a preference for one size or another, it should not be taken as "correct" or even preferred but rather, just an example of one you might make. Either way it certainly does the job.
It does seem that most modern naalbinding needles tend to be on the longer side of the range with 5 or more inches being common and I have seen at least one stitch where a longer needle would probably be an advantage.
To do the knitting itself please see these excellent Instructables
Knit like a Viking
On to making the needle...