I don't have a recipe off the top of my head, but here's our basic process. It took me a few tries before I realized just how simple this really is. If you can make muffins, you can make soap! ;) The links others have provided are great, and as in all things, YouTube is your friend.
Just like with muffins, where you mix your wet ingredients and mix your dry ingredients separately, and then mix them together, with soap you have two parts to prepare, and then, when the temperature of each is right, you mix them together.
Part 1: Lye and Water. When you mix these together, the chemical reaction creates tremendous heat and some noxious fumes. We mix them in a glass measuring dish, which we place at the back of our stove, under the exhaust fan running on high. After a few minutes, the fumes dissipate, and then you're just waiting for the mixture to COOL to about 110 degrees. This can take a while, so do it first.
Part 2: Fats. You can use any fats to make soap, from lard or beef tallow to olive oil. Most soaps use a combination of types of fats for different effects, and apparently it's the coconut oil that provides that soft, thick, lather than most of us like. We use a combination of coconut, palm, and olive, maybe with a little castor oil, rice bran oil, or shea butter if we're feeling fancy or have some on hand.
The oils/fats get put in a big stainless steel (non-reactive) pot, and HEATED on lowish heat until they all mix together and reach around 110 degrees.
Step 3: Mix. When the 2 parts are within about 5 degrees of each other's temperature, they will emulsify when mixed together. There is a lot of variation here; using lard apparently can take hours, mixing by hand can take a lot of time too. The secret is definitely in the stick blender. Buy a cheap one or a used one and dedicate it to soap making (although we did use our regular one for years and just washed it well, with no ill effects). Pour the lye water into the pot with the fats and gently swirl the stick blender around until you have a pudding-like consistency (this is called "trace" because if you drip some on the surface, it will stay put and be visible, not blend back into the mix quickly). Err on the side of a little runny. This can happen almost instantly or take several minutes. Then add your essential oils. Err on the side of runny-ness, because some oils (like our favorite, cinnamon!) can speed up trace and make the mix much thicker very quickly.
Step 4: molds. Now that everything is emulsified, it's going to keep getting hot for a couple of days. You need a mold that will withstand the heat, and that you will be able to get a solid lump out of easily. We use stainless loaf pans that we picked up at Goodwill, and then line them with parchment paper. You can use glass baking pans, cardboard milk cartons cut in half, etc. I would line any of them. Don't use plastic wrap, it can melt! Although, I think I usually do put a bit of plastic wrap on top, if I remember correctly.
Pour your "batter" into the molds. Now you want to keep the soap warm and encourage all of that heat over the next 48 hours or so. We wrap our loaf pans in lots of towels and put them in a warm place in the house.
Step 5: After a couple of days, unwrap your soap. It should look and feel pretty solid, and not be too warm anymore. Empty it out of the molds and cut it into whatever bar shapes you want. There is some internet fear out there that the soap at this stage is not safe and can't be used until it's cured for a couple of weeks. From what I understand, if the soap has completely "saponified" (ie, it's solid all the way through when you cut it up), it is safe. However, it will be very soft and dissolve quickly. So the last stage is essentially to dry it out a bit. The longer it cures, the more water evaporates, and the harder and more long lasting it will be.
To cure: spread the bars out on a tray in a ventilated area and leave them. We keep them on a bathroom counter for a couple of weeks, and then put them, on their cooling racks, in an unused cupboard. After a few months, when we need our racks back for other things, the soap gets stacked in the bathroom drawer or wherever. Presto! Soap for the year!
Around here, equivalent fancy soaps cost $6-8 for a tiny bar, and even with expensive health food store oils in tiny bottles, our bars might cost us $1. Not as cheap as bulk Ivory or whatever from Costco, maybe. But soooo much nicer to use.