The issue of release agents is not easy.  If you use grease, it can absorb into the paper and prevent further work.  I prefer one of two methods, depending on the shape.
1  damp paper with no paste.  Laying this over your original and then laminating with paste should allow you to lift it off when dry, providing no paste has leaked through.
2  Clingfilm.  This will work well on convex surfaces (eg the outside of a bowl), provided you lay it over the rim.  It will be very difficult on a concave surface (the inside of the bowl) because it will not hold in position.  Wetting the bowl for the latter might help.

Laminating the inside has the problem that the paper layers will shrink in drying (the wetter they are the more the shrinkage) and distort.  Laminating the outside means that it cannot distort.  In both cases it helps to take the laminate over the edge and then trim the edge you want when thoroughly dry.
Good luck

Using the inside of a form usually provides an easy release because the paper shrinks when it dries, as David said.  But it can also warp as it dries.  But you can reduce this warping if you fill the mold with something after applying the papier mache.  Glass marbles can do this quite well.  I have used the marbles that you can buy by the bag as supports for flower stems in arrangements.  Whatever you use, it has to be heavy enough to keep the drying paper in place but still allow air to circulate for drying.  I discovered that removing and replacing the marbles daily allowed for the shifting of the drying spots.

Even using paper strips on the outside of a mold can cause problems.  As the moist paper dries, it shrinks, and sometimes parts of the strips can pull loose.  This seems to happen more if you use heat to speed-dry the PM, such as putting it in an oven at the lowest temperature (personal experience here!).  Just remember to spend a bit of extra time pressing the strips down firmly as you build the layers -- there's no point to begging for trouble.

As Patraw said, cutting the PM off the mold has to happen when the shape is more complicated than something like a simple bowl.  The first thing to look for in your mold are "undercuts", which is a fancy word meaning that the shape "has its elbows sticking out".

Cutting the form off the mold is something you should do on a trial piece, just so fear of having to do it is laid to rest.  It's really no big deal, and once you practice a bit, you'll see how it works.  I really wouldn't advise you to make an important piece of work for your first cutting-off-the-mold project. You're bound to find a problem you didn't anticipate, so do a practice piece first.  Maybe several.

Cutting the form works best with strip laminating PM, as the fibers of the pulp method tend to catch as you're cutting.  Not impossible, but it is slower and needs a sharp knife and a steady hand, and patience.  It is easiest when the piece is still a fairly thin shell, strong enough to hold its shape when dry and not collapse when some pressure is applied, but not so thick that it is a trial to cut.  Nothing determines this like experience. 

Two tips...
1. Use an adhesive like PVA (white craft) glue or methyl cellulose that doesn't re-adsorb moisture easily when you form the shell base.  If you were to use flour-based adhesive, the shell is strong enough when thin ONLY as long as it stays dry.  If you add more PM to a thin dry shell, the shell absorbs moisture from the wet additions and can collapse.  No matter which adhesive you use, keep the applications of glue thin, not thick and soppy.

2. When you cut the form off the mold, don't separate the pieces completely.  Leave a connection in one area (a relatively flat spot is best, if available) to form a hinge, which will automatically keep all the cut edges in position.  If you cut it apart completely, it can be tricky to get all the edges back together correctly.  (We won't go into exactly how I know this...)

Sue

Patience... I've always want more of that.

Sue