Following this instructable should give you a good understanding of how to make functional heated apparel with minimal purchased supplies.

This project does require the use of a couple tools that not everyone has:

Soldering iron
Sewing machine

Having no experience using either one doesn't mean you can't start now, it just means your garment might not last as long or look exactly how you want it.

Step 1: Supplies

There are two general ways to approach this instructable, freestyling with found materials, or buying with intent. My friends and I have done both, first using found materials to see what we liked, which also informed us about what to buy for the next version.

These are the elements that you need to get started:

Resistive Wire
Either salvage this from a couple hair dryers, or purchase about 9' of insulated nichrome wire that is coiled inside of the insulation. The bought option is inherently safer, and easier to work with.
Battery
A Li-Po battery used for remote controlled planes works great, they are rechargeable, light, and can be found cheaply. The scarf in this instructable uses a 11v 1000mAh battery.
Switch
Not necessarily needed, but much easier than unplugging the battery when you don't need the extra heat.
Fuse and fuse holder
In the event of a short-circuit the scarf will draw more power and overheat, the fuse will burn out before anything bad happens. The rating of the fuse depends on how much heating you plan on doing. The scarf uses a 2A fuse, make sure it's a fast fuse!
Fabric
Cut up an old bed sheet, or pay a visit to a local fabric shop. Prices for fabric can vary wildly, and enough material can be had for as little as 5 dollars. The benefit of buying fabric is you can choose exactly what you want.
Insulated Wire
Last but not least, you'll need a wire that doesn't heat to complete the circuit and to solder to the battery connector and switch.

Step 2: Hairdryer Disassembly (salvage)

If you decide to salvage the resistive wire, you might need to dismantle two hairdryers to get enough wire.

The important thing to remember is not break the lengths if you can help it.

On some hairdryers the coils are very tightly wound, it's recommended to stretch them apart to get more length and to make sure the coils aren't pressed together in a bend.

Step 3: Wiring

The diagram shows how the wiring looks inside the scarf.

There are a few important steps in determining how to wire your own apparel, the temperature is determined by the length of the wire and the voltage of the supply. Seeing as we're using an 11 volt battery, we'll shorten the length of the wires if they don't get hot enough when plugged in, using temporary clips to test this is easiest.

Parallel wires

Sometimes at a temperature that feels nice the length of the wire is too short to cover much area!

The way to solve this is by running several wires in parallel with each other, just make sure they are the same length or else they wont heat evenly. The catch is that running another heating element increases the current draw of the device and reduces the lifespan of the battery. Finding a balance is key here.

Solder

When a good compromise is found, it's time to solder everything together. Remember to keep enough wire to complete the circuit.

Glue

A hot gluegun works great to insulate the solder connections, and to reinforce them so the exposed wire doesn't bend abruptly which could cause it to break over time.

Switch
Any switch would do, in the image above a small switch was soldered directly to the battery plug to save room, them reinforced and insulated with hot glue.

Step 4: Fuses

If you have a multimeter, measure the current that the device draws with all the heating elements wired together and get a fuse that is just above that rating. For instance, with a draw of 1A, get a fast fuse rated at 1.5A.

If you don't have a multimeter, buy a few fuses of various ratings, and work your way up from the lowest. Fuses are very cheap, but it might be worth it to invest in a cheap meter if you plan on doing more of this kind of stuff.

The fuse is highly recommended for safety, and well worth the couple dollars. Using insulated heating wire bought from a store almost completely eliminates the risk of a short circuit, but it's a great safety feature to have, especially when using salvaged wire. A short without a fast fuse could burn you or start a fire. Play safe.

Step 5: Layout

Test lay your wires over your project fabric.

Avoid crossing the wire over itself, for uninsulated wire this would short out the circuit, is bad even for insulated wire as it would cause hot spots.

The scarf pictured used almost 1m of the grey fabric and a half meter of the red fabric. Having a little extra is better than having a little less, no mater which fabric you're using.

Straight lengths were chosen for the scarf to get the best length.

Step 6: Sewing

Sew around the wires, not through them!

Cut down your fabric to a manageable size, stay oversized and cut off excess later.

Start by folding over your fabric and sewing in one corner of your wire harness. Then you can stretch it out and determine the length.

Sew channels for your wires to follow, this keeps their place and prevents shorts when using uninsulated wire.

Depending on how thick your fabric is, this might be as far as you want to take it, add a pouch for the battery to sit in and you're all done!

Our scarf fabric was thin, so we layered on more soft fabric to give it an extra plush feel.

Step 7: Layering and Battery Pouch

Making a pouch that will hold on to the battery is easy, even easier with velcro, but it can be scratchy and unpleasant.

Cut out a small rectangle to fit over the battery, then sew it to one side of the scarf along the sides.

We added a loop to enhance the function by sewing it to the same side, still being careful not to sew over any wires. The the rectangle is folded back over and sewn down the sides again.

This creates a pouch that the battery can't fall out of unless you pull apart the layers.

The last step in making it more plush is to sew on the outside layer. If you don't mind seeing some stitching this is really straightforward, but if you want to hide it you can sew on a fold of fabric backwards then flip the whole thing inside out. Using pins to hold alinement when you sew is necessary, pull them out as you sew the length. Take your time with this one as it has the biggest impact on appearance.