Another thought is to use garbage bags cut to the appropriate size which means enough to cover the insides and come overlay the outside walls of the container. Another suggestion is silicone bakery paper. This is a Teflon-like paper used to line cake pans. It can be purchased through some bakeries but gets ruined after one soapmaking project. This method is a must for making the sticker milk-based soaps.
Some folks suggest greasing the molds, but others say the grease is absorbed into the soap.
Other tricks involve coating a mold with a light layer of vegetable spray like Pam, vegetable shortening or Vaseline. Most times your soap will unmold with no problem, but the variable ingredients make absolutes impossible. Using a slightly flexible mold helps convince stubborn soap to release after receiving a gentle twist. One sure trick to make soap release is to pop soap and mold into the freezer 2 - 4 hours before attempting to unmold it. If you are using a huge slab or block mold, this could present some obvious space problems, but it does work.