Making Cold Process (CP) soap.

Oils such as olive oil are placed into a stainless steel or enamel stockpot.  A mixture of lye and water is added to the oils.  The mixture is stirred until it thickens a bit.  The mixture is poured into a mold.  The mixture hardens overnight.  It is then unmolded and cut into bars.

Plenty of beginner information is available from the links on the right.  Also, many good soapmaking books are available.  There is a large community of home soapmakers available online to help new soapmakers get started.

Detailed instructions for making CP soap at these sites.

Wikipedia (much broader overview)

David Fisher (About.com)

A Beginner’s Guide to Soapmaking

Miller Soap

Beginner Videos

Making Hot Process (HP) soap.

Making HP soap is like the CP process up to where the mixture is ready to pour into a mold.  Instead the mixture is cooked for about 1 and 1/2 to 2 hours hours by gentle heat in either a double boiler or a crock pot.  The HP soap is then put in a mold and allowed to cool and harden for several hours. It is then unmolded and cut into bars.

Detailed instructions for making HP soap at these sites.

auntroma.com

candletech.com

chickensintheroad.com

HP Soap Making – General Questions