What follows are some of the basic techniques that have been used for paper canoe construction, drawn from several sources. The techniques are all related to laminating strips of paper over a mold to form a hull. As modern paper canoe building is not a mature technology, you are still pretty much left to proceed based only on your own thoughts and any inspiration from what follows. You will need to work out numerous details.
Not covered is the "build it over a frame" technique used by Erhardt and others. (e.g. Ehrhardt, John, "Wrapping Paper Makes a Sturdy Canoe", Popular Science February 1951; also articles in 1950-'51 in The Rudder and The NY State Conservationist; see also Beebe, R.P. in The Rudder, January 1954, p49) Another approach is a more modern monocoque design technique found on Dave Friant's web site.
Paper: Many people start with a 36" wide roll of brown wrapping paper. A bandsaw can process this "log" of paper into 4 to 5 inch wide rolls. A rough edge may result at the cut, so the advice has been to sand the ends before you start to unroll it.
Mold: The canoes must be built over a mold or "plug" of some sort. Most molds have been existing canoes, although a mold from a cold-molding project might work well. (I don't know of anyone since the 1800's who has built a solid wood mold just for a paper boat, although one school group in Buffalo built a small newspaper canoe on the inside of a strip-built mold.) To protect the canoe you are using, you might like to purchase a very thin plastic sheet, often sold at your local hardware store as a disposable drop-cloth for painting. This can be stretched over the canoe and taped in place around the edges.
Tacking Strip: One suggestion (following in the tradition of the 1800's builders,) is to clamp, or otherwise attach, a wood strip parallel to but below the gunwales, (i.e. towards the floor if your mold canoe is upside down.) The strips of paper can be stapled to it as they are formed over the canoe. A great time to build a paper boat is when you have a wood-strip canoe under construction! Do your paper lay up over the stripper before gunwales are added and before it leaves the strongback. In any case, use something to hold the paper strips in place. They shrink as they dry and will pull up the edges of the hull if you don't restrain them.
Glues: Casein and Weldwood Plastic Resin Glue have good water resistance, but are a little hard to mix and/or spread. People have used brushes and small paint rollers to spread both. If they are mixed a little wet, (i.e. runny,) it helps matters out as the paper will immediately absorb some of the water anyway. Some folk have pre-moistened the paper or kept it damp inside of a plastic bag. If you use wallpaper paste, try one of the "higher-class" types. (They are all quite inexpensive.) In any case, try your glue and paper combination in small test panels. White glue & carpenter's glue have no water resistance, so you are just as well off with less expensive wallpaper paste.
Wrapping the Paper: The choice is yours! Some people have used lateral placement of strips (perpendicular to the keel line,) staggered so they overlap between layers. Others have used alternate 45 deg. placement of strips relative to the keel line, butting them together as much as the paper and the laws of topology allow. Coat a piece of paper, staple it at one end, smooth it in place and staple at the other end. For the 45 deg. wrap, make sure you alternate directions; the paper shrinks and will warp the hull if you don't keep things even. Stem and stern are left to your ingenuity. Some people have left them roughly finished, cut them open and installed a stem after the hull is off the mold. If you are using newspaper, you can probably ignore much of the above. The stuff is so pliable when wet, you can just paint it with glue and form it over the hull. (Almost like paper mache.)
How many layers? People have found that 8-14 layers of brown wrapping paper are required, depending on how thick the paper is, and how thick a skin you feel safe with. You probably want to laminate only 2 or 3 layers at a time, allowing the glue to dry well each time. Some have tried about 8 layers with a thin (e.g. 1/4 inch) foam or wood core material between layers 4 and 5 to stiffen the bottom sections of the hull, (as seen in some Kevlar and glass lay-ups.) Others have incorporated plastic mesh or cheesecloth into the layup. If you use paper alone and don't want too many layers, you will probably need to use floorboards, ribs, or some sort of stiffening material. Once again try it out first in a small sample!
Finishing It: The glued paper hull actually sands pretty easily. If you used white glue, you'll discover why people don't like it for strip canoes and, I presume, for paper canoes. It is sort of "rubbery" when you try to sand it and gums up the sandpaper. Sand the outside while on the mold. Remove it from the mold and work on the inside. Think through the attachment of wood parts and other components relative to painting or varnishing. Gunwales can simply be glued on the hull and the edges of the hull trimmed off with a sharp drawknife or a small saw. Some people add a few ribs to stiffen the hull and make it look more like a wood canoe. Mount decks, seats, thwarts, etc. as best you can manage. If low-cost is an objective, don't overlook the utility of closet rods and other materials at your local home center or non-marine lumber yard.
Waterproofing is essential. Thus a good grade of oil-based varnish or paint has been found to be useful. Recently, other waterproofing materials have been suggested, (see Dave Friant's site above). Some people have even used epoxy and also added a layer of glass cloth for greater strength and abrasion resistance.
This is pretty spotty, but as I said these are not instructions, just some helpful hints telling you what others have tried. (Remember the disclaimer at the top of this page.)