I essentially hold my thread, or yarn for the larger work, the
same as I do for crochet.
A bit of adjustment is needed when making the first half and the second half of the ds (double hitch stitch).
I wrap the thread over and around my left pinkie for tension,
and then up and over my first finger for working.
For me, this is standard crochet position.
I would think that whatever basic crochet position you use would work.
I make the very beginning of my Cro-Tat work with a normal crochet loop to anchor my work to the hook.
To make the first half of the ds, place the thread over the top of your first finger, bring it under and to the front.
Point your finger away from you and insert the hook under the thread in the direction your finger is pointing and pick up a loop onto the hook.
Snug this loop up and see the first half of the ds is formed.
For the second half of the ds, return the thread to the back of the first finger and bring it forward over the top.
Point your finger towards you and insert the hook under the thread in the direction your finger is pointing and pick up a loop onto the hook.
Snug this loop up and see the second half of the ds is formed, completing 1 ds.
Note: If your first pattern instructions are to chain so many stitches, then your beginning loop is not a problem.
If your first instructions are to begin right off in making a Ring, then you can count the first beginning anchor loop as part of your work, which I do in some cases, or ignore it as I do most times.