I've made trees in the past with chicken wire shaped around a wooden frame for the trunk (newspaper stuffed through the wire and taped in place to make knots), then covered it with burlap soaked in a glue and water mixture and painted it. I hung a large dead branch up high so the wires were hidden by the teaser, and added tissue paper "leaves." Tedious, but looked good -- don't know if I'd want to do it for more than one, though!

We made one tree frame like Chris did, but used crumpled paper instead of burlap.

Ooops I forgot to mention that I made up a ‘Fotheringale’ dress cage, for the base of the tree. Held up by the straps inside, to assist the dancers leg & feet movement.

There are a lot of ways to make 3D trees onstage, and for each of your functions a different method may work best. 

The most common, easiest and probably cheapest way has already been addressed... build a frame of some sort and drape it with fabric and glue water.  To thin out the glue, add water until it is the consistancy of a heavy cream... it will probably be about 2 parts glue to 1 part water.  Something that hasn't been mentioned is that you want to use white glue and not carpenter's glue, because white glue provides some flexibility, so it won't crack off the surface of the fabric with use.  Burlap is a great textured fabric to use for this purpose, and if you dye it different shades of brown first, the painting after draping can be minimal. 

I don't recommend the chicken wire.  It isn't really all that sturdy when installed and provides a lot of sharp points that can injure both actors and costumes.  I prefer to use a stiff screening if I decide I want a more firm base than the glue water fabric can provide.

If the fabric is too plain in texture for you, you can add texture over it before painting.  One of my favorite texturing items is a rubbery roofing compound called Jaxsan, because it's flexible to not break when scenery moves and it's durable.  Joint compound mixed with white glue (to make it more flexible) is cheaper and similarly effective.  Either one will make your scenery heavier, but sometimes that's ok.

Another option is to apply layers of blue or pink insulating foam over the frame and then carve it to the shape of a tree.  You would have more control over this process and if sealed properly with a product such as Sculpt or Coat, this will provide very durable trees that will last for many productions.  This process will be more time consuming and expensive.

For smaller details on the trees, look into using plaster bandage, which is very easy to manipulate when building the tree, but dries quite durably. It can be found at your local craft store. It's a little heavy for large scale use.

Another material that can come in handy for building organic things like trees is spray foam, like "Great Stuff," which is used for insulation in the cracks around door frames and window frames in real life.  It is perfect for sealing in cracks in plywood surfaces... or if you piece together some of your trunk out of luaun and ply scraps, it can be applied between gaps.  It expands and then is carvable in a couple of hours with a simple breadknife and rasp.

For the trees that are manipulated by actors, you may want to consider a combination of puppetry and costuming where you actually cast the trees.  Think about Lion King costumes and how some of the large animals moved... trees implimented in a similar fashion could be really stunning visual elements that also allow you to involve more people.  (Run a puppetry workshop to get people interested and excited in that aspect of theatre... show videos of some of Julie Taymor's puppetry work as inspiration.) 

Larger hand umbrellas with the nylon removed and the wire parts bent appropriately can make a nice base for tree branches that are light and able to be manipulated by people.  Then the wire can be made into more realistic tree branches with plaster bandage, paper machier, or a variety of other substances.  I've also created trees out of beach umbrellas in bases before, and that worked very well, although when I did that I made them into palm trees for Seussical and the actors carried them on stage looking like folded beach umbrellas and it was only obvious that they were palm trees after they were popped up, which was a fun surprise for those watching and an example of how scenery can add a little bit of humor from time to time.

Another option is to not go too realistic, and instead stylize the entire set design especially in Neverland.  Stylization, if carried out consistently through a production, can provide an inexpensive way to achieve stunning scenic effects.  It allows the audience imagination to be more active and will also allow for mistakes to be more easily hidden.  Everyone knows what a real tree looks like, but if your trees are more fantasy based, the audience will never know if you've fallen short of the initial design.  For example, what if trees in Neverland all had glossy purple bark created out of vinyl and instead of small green leaves they have flowing red and pink foliage made out of feather boas?  Because the characters have travelled to a mystery land, it is ok to throw realism out the window, and your audience will applaud the fact that you went somewhere unexpected.  The more unique take on the design and the brighter colors will help surprise your audience and therefore entertain them more.

One option for the hollow places in trees where you want actors to be include incorporating trash cans into the structure.  Another option is for some of the scenes to take place with actors in a treehouse, that has branches growing around it, but to not actually show the rest of the tree structure... whether that would work depends on your blocking. 

Another random thought I've had is this:  I wonder if there's a way to create effective stylized trees based off of pop up tents.  Sew fabric bark to the tent surface, and when you want to see actors inside the tent open the door.  (You're lighting designer may need some specials to light actors inside a structure.)  But, when they are hiding, they can zip up and truly become invisible to bad guys.  I've never tried that, so it might not work, but if it did it could be very fun.  All of the foliage would have to be very lightweight.

Anyway, I hope that was helpful.  Best wishes on your production.

Laura

Laura