Have not tried olive but I have done lots of cuttings. I would say that right now would be an excellent time.
Select branches that grew fast, and all this last year. (one year old wood.)
I like to prepare the cutting before I actually cut it. In this case, remove all but 3 to 5 leaves, leaving only a very few at the tip. Do this a day or 2 before cutting. This way the tree can provide the sap to help heal the leaf breaks, instead of taking strength from the new cutting.
If you can find some really vigorous growth that grew all last year, (all in one year, usually a lighter or more green color) you can do the cuttings without leaves at the tip and will probably have better success. Nice thick stem branches are the best.
Take cuttings about 8 inches long. Be sure that you will have at least 2 (3 is better) nodes below ground and at least 2 above ground.
Use a rooting hormone, like Rotenone (not sure I spelled that right) and lightly powder the part that will go in the ground, about 4 inches worth, with at least 2 nodes.
Plant in good potting mix. I like to plant at a little angle, not sticking straight up, as this seems to give the cutting a better rooting start.
Give a warm sunny place, making sure the potting soil does not get soggy or dry out. When days are a little too hot, sprinkle with cool water to keep them from scorching.
Let us know how it turns out, and good luck.

Thanks for the great advice!

cd