Cut off a piece of stem, remove the lower leaves, & stick it in the ground. You can also root them in water. If it is warm, they can wilt, so water rooting may be better. You can stick the entire cutting in water to refresh it, & when temperatures cool off, stick the roots only in water.
Bush & dwarf varieties root this way. Dwarf varieties also propagate easily by rhizome division.

You didn't mention what kind of Mexican Petunias you have- I have the tall purple mexican petunias. Basically, as long as your plant has flowered once, you can cut off about 6 inches from the top, cut the leaves all in half to reduce stress, then slice the cut end up about 1/2" to 1 " to allow more water to be absorbed. Stick the cutting in dirt in sun and just water a little daily for 1-2 weeks. By then you will have roots and the plant is on it's own. You can also easily propogate by dividing roots. I found that when rooting the Mexican Petunias I have in water- they drop leaves and sag.

I forgot to add that I add an airstone to my water, which may counteract wilting. You should wait until after they flower, but when mine break off they root this way. My variety is the tall purple  the dwarf I divide the rhizome.

Air stone is new to me, could you please describe and thanks!

ps. I'm also gently dividing out some hearty but strong pieces; I just rediscovered I had some that I pulled 2 weeks ago left, left them outdoors in a container of water, that still look great for planting!

I think the air stone just keeps the water fresher for longer. I've read about that too, but honestly, I get plenty of success without additional devices added to the simple cup of water. It's certainly worth to try if someone wants to, but imo, not necessary. An example of the simple water container doing the trick is from your own bunch of stems left outside without nary a person caring about them, and they still look good for using as a new plant.

In my case, I just cut some of the tops off the growing tips. That lets the remaining plant make branches to grow out and I get some stems to root for making more new plants. I've rooted them in water or sticking them in the ground (and keeping it moist). This is one of the easier plants to root.