For pomegranate and fruit trees in general, you'll want to take cutting from the branches of the year (still green, or just starting to gain lignin). Plant cells in green branches have higher differentiation capacity and will switch to root cells more easily. Doing it at a proper time of the year and day is also important, so it doesn't rain on the injuries you just made on your tree, and so that it's not too hot for the cuttings to handle the rooting period.
Choose them as straight as possible, as trees don't extend - they grow on top of what's there already (so any twists in the branch will stay at that height).
Make sure to make clean cuts diagonally to the stem, so they have a bigger surface area for water absorption. Disinfection (soap water) of your cutting tools may be necessary, even if there's no visible funghi or decomposing/rotting organic matter on the branches.
Clean out any leaves on the lower part of the cuttings, making sure to maintain leaves and/or at least 3 buds on the growing tip.
Rooting agents: salicylic acid is the most important hormone that plant cells produce for rooting. You can use it to increase the likelihood of your cutting forming strong roots.
WTF is that, you may ask - well, it's a substance you can fin naturally in young willow shoots or branch tips. It's also used in aspirins.
So you have at least 3 ways to go about getting it:
Purchasing rooting agent (usually a powder);
Dissolve an aspirin in water and dip the cuttings;
Get willow cuttings, peel them, and leave them in water for a couple of days along with the soft bark you removed.
Now, you'll want to give the cutting good conditions for rooting - avoid low/high temperature extremes, and keep the rooting part in the dark, with controlled moisture - not enough for funghi, but not letting it dry completely for more than a day.
Good luck!