Soap that we use every day is created with an amazing chemical reaction. For the details, check out a description by the Soap and Detergent Association. On the one part you have a lye/water solution and the other component is a combination of fats. The important thing is to get these two combinations to approximately 100 degrees F (I got this tid bit from Susan Miller Cavitch's book). At that point you take the two liquids and combine them in one large stainless steel bowl.
Now the next tip is to use a hand blender- they are useful ;) (I got this tip from Al). This tool is essential for two reasons: you have to get the mixture combined before it cools and it is much safer to use then hand mixing and splashing the caustic lye solution all over your work area. You know you have soap when you get a trace - when the soap gets a consistency such that the ingredients are combined together and you can see patterns on the top of the surface (again for more information look at walton). I think that the mixing is the best - it is when you get to visualize the chemical reaction and have successfully made soap.
There is an easier way to make soap. This weekend I had Ina and Maleeha over and we happily created translucent soap creations. To get the equipment requires a trip to your local Hobby Lobby or craft store. There you can find a block of translucent soap without scent or color- your "blank canvas" There are also scents, but don't get the colors there - regular food coloring works just fine! The only other required item is some type of mold. For these, candy molds, styrafoam egg containers, etc will work just fine. Again, the local craft store will have some cute molds to choose amongst.
With translucent soap, just add a bit to a microwaveable container and melt in the microwave. A little time goes a long way here. I'd say for about 1/2 cup soap give it 20 to 25 seconds. Try not to make it boil too much ;) Now add scents and small amounts of coloring- again a little goes a long way :) and stir with a metal spoon- pour in molds and wait until the molds are cool to touch. If you are making a big mold, to save time, you might want to put the mold in the freezer temporarily (or here in winter, just place it outside for a bit ;) )- just make sure that the mold is not brittle when you try to remove your soap from the mold- you might let it warm to room temperature.
So that is how you make soap. There are three books that I use (two mainly: The Soapmaker's Companion and The Complete Soapmaker) and a fountain of online resources with good recipies, recomendations and tips.