Yes, and no. They may be extracted, pressed, or produced in other ways, but the processes by which they are made is fairly complicated.
Well, there is a lot of confusion over what essential oils are, in the first place. And a search on the topic just yields a variety of opinions, and the more you study it, the more confused you get!
At its most basic, an essential oil is merely a plant oil. Not all plants HAVE sufficient oil to obtain a pure oil. So they are distilled, extracted, infused, pressed, or otherwise obtained from plants, with or without the assistance of an extraction substance (water, alcohol, oil, solvent, etc).
So what we are after is not necessarily an "essential oil" that is made at home, but something that can be used in its place.
Most essential oils are highly diluted, even though they are used as, and sold as, a concentrate. This is the first thing - they are already diluted.
So if you want a substitute, you can use something that is not nearly as strong as a full strength essential oil.
I know of four ways to get something that can be used in place of an essential oil, depending on the use and required attributes, two of which can be used externally, two which can be used internally.
1. Oil extraction. This is like making a tincture, but with oil. It can be done on low heat in a crock pot, and I just put water in the pot, and set jars in the pot with the oil and plants in the jars, with the lids on. Does not stink up the kitchen, keeps the temp low, and takes about 3 days to make a pretty strong extraction.
2. Honey or Sugar extraction. Same thing as an oil extraction, but with water added. You can end up with some pretty smelly stuff this way, but it is generally only good for those things that need sugar anyway - in other words, best for internal use.
3. Alcohol extraction. This is very common, and results in a tincture. Smells like the plant, but with an alcohol base.
4. Syrup extraction. I do this instead of sugar extractions. And I do it in an electric pressure cooker (takes about 1 hour that way, no stirring). Easy to do, 1 cup of water to 2 cups sugar, and about 4 cups of plant leaves, petals, etc. Very useful for internal medicinals, and a great replacement for alcohol tinctures.
I have no patience with long and intensive procedures, but some say you can make an essential oil with a distillation system. You don't get a really strong one unless you are really patient and know what you are doing. So that is another option, if you have the patience and knowledge to do it.
The point is, if you know WHY you need it, you can probably make something that will work instead, that will allow you to get the job done.