A Google search got this:
new plants can be grown by taking stem cuttings with at least two joints. Cuttings can be then rooted in pots of sand and peat moss mixtures. These pots then should be placed in greenhouses with bottom heat of 70-75 degrees.

During the rooting process they should be kept out of direct sunlight. Once rooted, the plants can be transplanted to larger pots or directly outside in milder climates.

A second way to propigate Anthurium is to take stem cuttings particularly from trailing varieties and place them in water. In four to five weeks the plant should develop roots and can be transferred to pots.

The final method is through direct planting of mature seed or berries.

Good luck.

A leaf (or leaf+petiole) isn't enough. You need part of the stem, too. They'll root in water or soil, if given proper care, though both are (in my experience) slow processes. Most commercially sold plants are a group of plants, or one plant with a lot of side shoots: individual plants within the pot can be separated and potted up on their own. Division is faster and less risky, but more invasive and messy.

Neither stem cuttings or division are recommended for plants that don't actually belong to you. Which I'm sure you know.

Check the plant again to see if it might have an offset. It'll look like a little replica of the big plant...a new plant growing from the side or base of the 'mother' plant.
These offsets will usually have a few aerial roots attached.

Have you checked your area WalMarts lately?
There were many Anthuriums for sale at the one I recently visited.

Yes, anthuriums must be the plant of the month because I've seen them everywhere. If you have a Lowe's nearby, they discount their anthuriums if they've had them a while and lose their blooms. I just bought a large one for $4.00.

Susan