When lining your mold with freezer paper, I see other soap makers go to a lot of effort to cut in geometric angels into the paper so that it will fit into the corners perfectly. You should be able to fold your paper into the ends to get the same perfect corner.
One day, when the grocers ran out of freezer paper, I tried plastic sheets. These were actually black garbage bags that I cut easily with scissors. And how to line a soap mold with plastic, was at first, a little more difficult to use as the plastic was flexible and therefore fell down inside when I wasn't holding it up. But with time and many hundreds of mold linings later, I prefer the plastic because of this same flexibility.
Cutting plastic sheets to fit the corner are not necessary here either. It is fairly easy to bring the plastic excess to the ends where you can tape it down. You can reuse these as well.
I've seen other people use wax paper, but this type of lining disintegrates and you will be left picking off lots of little wax paper pieces off your soap slab. Use only if your soap is ready and you have nothing else as a liner.
Plastic wrap, the type used for food, is one that I used only once. The caustic soap base somehow leeched the flexibility out of the plastic, perhaps into my soap, as this plastic wrap was a little brittle after this one use.
Perhaps the best 'how to line a soap mold' is to not have to line it. The new molds that have came out since I started making soap, include a Press-Lock type mold, and Plexiglas molds. Either one of these will eliminate the need for lining a mold, and these will easily come apart. Another benefit is that your soap slab will have a clean edge, and not have any markings on it that may occur with any bends or folds in liners. But, the price of the Plexiglas mold is extremely expensive, a 3 log mold may cost you up to $250.00.
Just in case you are considering pouring your soap base into a regular mold with no lining - Don't. I did this once, and I had to scrap the sides of the soap between the soap and the mold in order to loosen it from the mold.
How to line a soap mold with no creases or folds in the lining material can be very frustrating at first. Some people do not like the fold lines or creases that may appear on your finished soap log, understandably. If you are careful with pressing down your freezer paper or plastic sheet, these will be kept to a minimum, or almost invisible. If you do leave creases and folds in your liner, these will show up on your soap as well. The same goes for the corners of your mold. I always spent the extra few seconds to make sure the liners were fitted nicely into the corners so that the finished soaps had nice and tidy 90 degree corners.
With the creases and folds in the end sections of your soap, save these creased pieces for your use, or for dicing and adding to a new soap base. For instance, I would keep all my earthy scented scraps like sandalwood and ylang ylang in one container, then add these pieces to soap base, add a little more scent, and get some of the prettiest looking bars when they were barred.
From "how to line a soap mold" to what you can use as a mold . . .
Info on digital scales for making soap.