Oakleaf hydrangeas doesn't roots from cuttings as easily as all other hydrangeas, not to saying that it's impossible, though.
Groundlayering would be your method of choice.
Anchor a limb to the ground in a spring, cover it with soil (tip of the limb/cane must be above the ground), mulch it and by the fall you'll have a nicely rooted young plant.
Leave it 'as is' for the winter (you may pile some extra mulch for extra protection) and in a spring severe it from the mother plant. Plant it and you are done!
Good luck.

Thanks for the information. I have rooted other plants that way. I just didn't know if it would work with the Oak leaf hydrangea. I'll go anchor me one down this spring. You don't think it would do to anchor one in the winter?

Happy Gardening,
Marian

I have about a 33% success rate with cuttings. I take cuttings in May (I find the slightly woodier cuttings do better than the very soft green growth). 15 cuttings two years in a row and got 5 plants each time. I think I could do better next year now that I know to avoid soft wood. I didn't have much luck with layering.

This species of hydrangea is extremely easy to start from seed and one spent flower head taken in mid to late November can produce thousands of plants.