Excellent answer already from grfrazee, just wanted to add some practical options.
The tool to use would be one just like this (but not necessarily this one):
I see in the Comments that you say this isn't terribly expensive but I'd like to offer a cheaper alternative to anyone for whom $50 or so, for a seldom-used tool, might be a bit much. Behold:
Yes, those are just a common nut and bolt. But using the same method outlined in this Answer the bolt can easily be turned into a tap, and a very good one at that.
For the nut you do the same basic thing, you file a groove (or more than one) in the threads to make cutting edges and provide clearance:
As important or more than when using a commercial tool-steel tap and die, lubricating the threads with oil when doing the cutting is highly beneficial. A range of oils have been used for this in the past but mineral oil/liquid paraffin is probably the most common choice these days. Also as with a commercial tap and die it's important to reverse direction periodically to clear swarf.
A slightly more involved method is shown step by step in this article on WK Fine Tools. A basic wooden holder for the filed nut as shown in this (taken from Le Menuisier Ébéniste by Roubo) could be advisable, but is not absolutely essential.
More general information and some useful details on tapping and threading wood in this piece from Christopher Schwarz, Tapping Threads Without Tapping Out.
And a ## Heading ##bonus for those inclined towards cheap solutions...
Make your own dowels
Dowels can quite easily be made using various homemade and commercial tools and setups. Other than the potential cost savings it allows you to make your threaded rods from species which aren't offered commercially as dowels.
One basic technique is an old method, and involves bashing square wood through round holes:
Photos showing the method in use:
Note: shop-made plate in the top image, commercial plate below.
On the same basic lines but with a modern twist (pardon the pun) this method demonstrated on Lumberjocks by user stefang, using holes drilled at 45° through a mild-steel plate and a drill to spin the workpiece.
Dowels can also be spun through a jig/tool that cuts them round:
More reading on the pencil sharpener method, on Woodgears. And these two entries on Lumberjocks, one and two.
There are also various router-based methods that are worth investigating for those who own a router.