I could do a pictorial fairly easily, and maybe a video if I could get someone to film for me, but my Flip doesn't have great resolution.
Probably the easiest combo to start with would be olive oil, palm oil, and coconut oil. Simple and reliable. Let me dig out my recipe cards and try and find some lye--Lowe's is supposed to carry one brand last I checked.
A good scale is a MUST, and the higher it goes the better.
Supplies I must have (your mileage may vary):
Heavy pot for melting solid oils
accurate scale that measures small increments
large plastic pitchers for mixing lye solution
STICK BLENDER--cheap one, dedicated to soaping only
mold, lid and liner--can be anything from tupperware to a Pringles can
large bowl or plastic bucket for blending soap to trace
tons of paper towels
rubber gloves & safety goggles
towel for wrapping/insulating mold
at least a gallon of white vinegar in case of lye spills
Be prepared for a good spell of waiting once the lye is mixed--you won't be soaping all at once. You'll mix your lye and water first, and it will get REALLY hot. You'll have to wait for the lye water to cool down before you can add it to your oils, otherwise your soap could asplode.
It takes a long time for the lye/water to cool down, and you'll need a very safe place to keep it while you wait. This is the most dangerous part of the entire process, IMO.