At a minimum, you need veggie oils & lye; many recipes add essential oils later in the process for scent.
You could make a simple hand soap with olive oil & lye.
http://candleandsoap.about.com/od/soaprecipes/a/castrecipe.htmOlive oil is available at grocery store, lye at the hardware store. Make sure you read the labels closely to be certain there are no adulterants; only use 100% sodium hydroxide (or potassium hydroxide, which would be unlikely in the US.)
Both are available in sufficient quantities for a few dollars each. However, I have found the reagents usually cost a fraction of the cost of the necessary equipment. Soap can be made with ordinary cooking pots & pans but I wouldn't ever use them for food again. Don't use pans with any kind of interior coating. Stainless steel or glass only. Do NOT use aluminum utensils or vessels with lye.
The following is both general advice & specific to making soap in a household where surprises are commonplace:
Before you start make an inventory of all required items & arrange them appropriately. Be sure you understand the sequence of steps & risks. Identify where in the process things can go wrong, have a plan to deal with it. Wear old clothes. Use gloves, goggles. Lye is unforgiving. Have a 5 gallon bucket partially filled with cool water for emergency cooling of the pans (about 1/3 full). Put away pets or send them outside. If you live with others or guests may arrive, make sure you tell them beforehand what you are doing. At my house, cooks always have the right of way & the authority to expel anyone from the area without notice.
Commercial dish soap & detergents usually have surfactants which can reflect a substantial portion of their cost. I'd suggest being comfortable with making hand soap before trying liquid soaps. Although you might try cheap detergent by putting some bath soap chips in warm water & adding some washing soda, stirring til it is all dissolved.