In order to answer that, we need to know if you are interested in making Cold-process, Hot-process or Melt & Pour.

Weldontx,

You'll require for cold processed soap (better known as CP):

An accurate scale;
Microwave large enough to melt the fats and oils
Plastic pourable containers; 1 for lye solution, and 1 for your fats/oils;
Small container for scent (if using)
A couple of Large spoons; 1 to mix the lye solution; 1 to bring the soap to trace/Stick blender; a large spatula may come in handy also for scraping out the soap into your molds;
Mold(s) to accept the raw soap;
Paper towel for cleanup;
Ingredients of course, including sodium hydroxide, fats/oils, water, scent

Notes (random thoughts):

An accurate scale, probably an electronic one, definitely not a spring scale; I use a triple beam scale, the cheaper way to go is the electronic scale accurate to the gram or fraction of an ounce (I prefer it to the gram). Also, make sure that it has a tare feature.

You can stir the soap with a large spoon (this depends on the size of recipe of course) but a stick blender is preferred; get one from a second hand outlet, Braun is a good second hand choice.
The stick blender is much faster than a spoon for bringing the soap to trace.
Glass/Pyrex is good for measuring and holding your scent (if using a scent).
I prefer pourable plastic containers, especially if the plastic is the heavier type, Rubbermaid comes readily to mind, and also second-hand outlets are your friend.
Ice cream containers are what I occasionally utilize for different aspects of soap making.

Use a fairly flexible mold for forming your soap, or one that you can destroy to get the soap out; IE, a milk carton (is a great first choice).

Pick a recipe with 2 or 3 oils you can get easily; olive, coconut, palm, are just some of the myriad of choices you can make.
I won't check your numbers, but if you like I can look over your recipe and give any tips. You'll need to use an on-line soap calculator to make your recipe, or find a trusted recipe.

You can get started fairly cheaply; after the scale, the scent is usually the most expensive part of soap making.

Never use aluminum equipment with the lye or after the lye has come into contact with the fats/oils; this will ruin your soap.

I may have missed something here, if you have any questions just ask!

I agree with ronniner, except I use a couple of different things in my cold process soapmaking. For the lye solution (mixed with distilled water, of course), I use a 32 ounce Pyrex glass measuring cup, because the lye solution reaches temps over 200 degrees when it reacts with the water.
I too, use a large plastic mixing bowl for combining the lye and fats/oils, but I got even cheaper with one of the large plastic bowls from Dollar General, and it's been working great for about 4 years now.
I got my electronic scale from Walmart online, and it's accuracy range is within 1/10 of an ounce. This accuracy level will work if you are making at least 4 pounds of soap with your batches. You do have to be a little patient for the scale weight to settle in, but it also does tare weighing, too.
This is important because many times, different fats/oils must be weighed in separately, to accurately calculate the total amount of lye needed (and water).
Another good hint for making good soap is to use either some coconut oil, or palm kernel oil in your batch, to harden, and especially enhance the lather. Again, Walmart sells a brand of coconut oil called LouAnn that works great for me, and you don't have to buy large quantities of it online.
You will have to buy your lye online, though - at least I have to. I bought 32 pounds in 2 pound containers a couple of years ago, and I still have about 8 pounds left. Most of my batches are around 5 to 7 pounds, so on average, I end up using about 12 ounces of lye per batch (depends on the recipe, of course).
There's only one bad thing about soapmaking - people fall in love with it once you've made some good batches. My wife and I won't ever use store bought soap again, and other family members/friends can't ever get enough of it.
I hope that your soapmaking is as rewarding to you, as it is to me. I don't sell too much of it, but it doesn't matter - it's great for yourself, family, and friends. It makes wonderful gifts, too. Enjoy it, my friend!