There are many materials designers, hobbyists, and tinkerers can use to build physical prototypes. Some require access to specialized tools to professional workshops, but some can be worked by hand in an apartment. Below are a few ideas with varying degrees of complexity.
Note that New York City and NYU have a wide variety of Fabricating facilities that could be of use in creating prototypes.
A glue gun is a thinking man's hammer. Its amazing how many things can be stuck together with such a simple device, plus a few glue sticks. For holding together prototypes made on the cheap with fabric, paper, cardboard, foam board, or other light materials, it is indispensable.
Paper, Poster Board, and Cardboard
Dont be afraid to use cardboard boxes, cartons, and other thick papers for your projects. These are great for sketching ideas without spending a lot of money. Paper and foam based materials are lightweight, which means you can hold them together with glue and sticky tape.
Foam and Foam Board
Foam can be easily and quickly cut with a knife, scissors, or with a specialized heated foam-cutting wire, into whatever shape you want, plus you can easily stick things like thumb tacks, nails or other sharp objects into it.
Foam Board is a very useful foam/paper combination similar in purpose to cardboard, but thicker and more shapeable due to its beneficial layer of foam. See the RISDpedia for a good description of how to use it.
Both are available at any good art supply shop.
New York once had a vibrant garment district. You can still find remnants of it on the west side of mid-Manhattan and it is a good resource for your fabric needs. RISDpedia has a page devoted to fabric stores in the city.
With recent developments of flexible LCD screens, conductive thread, and other flexible electronic components, sewing is becoming an increasingly useful skill for designers who wish to make wearable or other textile-based electronic components. You probably know somebody who knows somebody whose mother has a sewing machine. Try to get access.
Weaving, knitting, crocheting, and other fiber arts techniques are ancient practices with millennia of wisdom embedded within their practices. When you cant find the textiles you want, make them but its time consuming. There is no lack of knitting meetups in the city, and there are digital loom services online that will weave any pattern you design for a fee, of course.
Recent developments have also made digital printing on fabrics an affordable option for creating novel patterns. Online services abound, and there are some shops in the garment district that offer this service. Spoonflower.com is one such online digital textile printing service.
Molds and Casts
Casting is the process of taking a mold and filling it with whatever material you want to make something from, such as clay, resin, silicone rubber, plaster, hot glass, metal, concrete, or other liquid or semi-liquid material.
The Complete Sculptor, a specialty store in New York, sells the necessary materials and has classes and some useful information on mold making and casting. There are many great videos on casting techniques available on brickintheyard.coms YouTube channel.
Smooth-On.com also provide information, products and How-To advice on casting and mold making.
Ceramics, based on clay, can be used to create interesting and beautiful forms for inclusion in your projects. Many ceramic artists work by hand, or with minimal tools, and require only a few pieces of equipment, such as a pottery wheel and a kiln to create a wide variety of forms.
Sculpey, a synthetic clay-like material, can be shaped by hand and baked in a conventional kitchen oven to create small ceramic pieces.
Plexi Glass, Acrylic, and Plastic
Plexi glass and other plastics can be drilled, grinded and otherwise shaped more easily and quickly than true glass. But please dont do this at home it can be messy and it is toxic to breath in plastic particles.
Glass is a luxury, but can be more approachable than you might think. Cutting clear or colored pieces of flat glass is the basis for stained glass, and can be done easily with an inexpensive glass cutter. Wear gloves.
Blowing glass is a wonderful and ancient practice. There are several place in New York that provide glassblowing and other glassmaking facilities and classes, including Brooklyn Glass and Urban Glass. Hot glass workshops tend to be very expensive to rent, although for small things, flameworking is a hot glass fusing and blowing technique many people do at home to make scientific, artistic, and even drug-related glass pipes and vessels.
Besides blowing, there are also fusing and slumping techniques, which involve heating and melting glass to create custom forms in a kiln. Small kilns for melting glass at home are becoming available at affordable prices, and some kits even let you fuse small glass pieces in your microwave oven.
Laser cutting & etching
Laser cutting can be used to cut or etch highly detailed designs into a variety of materials, including many woods, plastics, glass, stone, and some metals. There are many online services that will laser cut your designs into materials of your choice. For example, outfab.com offers cutting services at a flat rate.
NYUs Advanced Media Studio (AMS) provides laser cutting services. Projects require approval from AMS, and they provide guidance for how to properly prepare your designs for the laser cutter.
The last few years has seen an explosion in the commercialisation of personal 3D printing machines, thanks to companies like Makerbot. These machines allow you to print 3D objects, mostly in plastic. Thingverse hosts a gallery of things made with these machines.