I've used double-sided duct tape. This has the advantage of having a fairly thick (heavy) fabric layer between the two adhesive faces; that makes it more rugged. Other kinds of double-sided tape have only a thin layer of paper or plastic holding the two adhesive faces together.
The tape I've used is Shurtape. I bought it at Lowes, and while I haven't looked for it recently, I presume they still carry it. The last time I saw it, it was on an upper shelf (well above eye level) in the tapes and adhesives area. Shurtape has a removable blue film over the outer adhesive layer.
My experience has been that it works reasonably well - recognizing that it is only adhesive tape and not a more positive fixing. One hint - make sure both surfaces are flat and clean (especially, make sure that there is no dust on the faces), apply the tape to one side, peel the film away, and then press the other side in place. Put under pressure for a few minutes - clamping is ideal, but holding the 'glueup' in place with tailstock pressure for a few minutes is fine. But the key is to wait a few minutes before starting to turn. Ten minutes should be sufficient to allow the adhesive to set up.
I try to keep the tailstock in place as insurance whenever I'm turning. When it is necessary to remove the tailstock to finish off a piece, use very light cuts.
