The axle is held in the drill in the same fashion as a regular drill bit.  It is then spun at high speed while you use various tools such as files, sandpaper and polishing compound to perform the speed modifications.

The wheels are placed on a mandrel which is then placed in the drill.  The wheels can then spin while you perform modifications.

The drill is used in its more normal fashion here to drill weight holes and other design holes in the car.

With axles, the dremel is used primarily for polishing.

There are over 50 different drill bits that can be used with the dremel, all available at the local hardware store.  More common bits that I have used are a round, rough sanding bit to sand inside holes, a round cutter bit to dig out holes, router bit for grooves and engraving bits.

Without giving away too many secrets here, simply stated, the dremel is used in the testing procedures for the wheel and axle combinations. 

Coarse Sanding (Low grit levels; 60 - 300 grit)
The lower grits are used for sanding the car body.  One starts with lower, very rough grits and slowly progresses to higher grit levels. 

Medium to Light Sanding (Medium grit levels; 400 - 600 grit)  These grit levels are used for sanding of the car body as well as sanding the wheels and axles.

Fine Sanding (High grit levels; 800 to 1500)  These higher grit levels are for specific car body finishing, wheel sanding, and axle modifications.  Not commonly found in hardware stores. 

Steel Wool is used in various wheel and axle modifications to get into corners and other areas not so easily modified with sandpaper.  It is given single digit numbers and "0" levels to show grit.  A 2 or 3 is for rough sanding while a "0" is for medium jobs and "0000" for finer work.

My son's favorite power tool, the electric sander is a wood eating machine, but a very safe tool to use with the right age groups and adult supervision.  Use the mouse handheld version with the tongue attachment for close-in work.

A scroll saw is very nice to have as it can cut turns, waves etc. for fancier car designs.  It can also be used to cut intricate hole shapes. It is a fairly expensive tool (approx. $100 or so) and a big tag for a once a year job.  It is certainly not a necessity.

A band saw uses a wider blade and is a more general cutting tool than a scroll saw.  It is more powerful and faster but produces less intricate cuts.  It is higher in price than a scroll saw and nice to have, but not a necessity.

The coping saw is a manual equivalent of the scroll saw.  It uses small blades and can make small turns and more intricate cuts for fancier body designs.  It would be considered a necessity for intricate cuts absent a scroll saw.  It is less powerful than a regular hand saw and will take  a while to cut a car body but is fairly inexpensive.

The basic wood saw is the best tool to use for generic wedge design cuts with minimal intricate patterns.  More powerful than a coping saw and quicker.  Not as exciting a design but very popular and very  fast.  More likely tool to already have.

As stated above, there are a number of specialized cutting bits for the dremel tool.  Most costs about $6 or less in a local hardware store.

Steel weights come in a variety of sizes and are commonly packaged in a stick-on format.  They are not as dense as lead and therefore take up more space to apply the same weight.  It is best to use more dense materials to apply weight in a more compact area.  This website is all about speed and steel weights and speed just aren't used in the same sentence with true derby enthusiasts.

Lead has its safety concerns with handling but is more dense and is available in easy to use cylindrical and flat forms.  It is soft and can be adjusted (hammer, pliers etc.) into a myriad number of shapes to fit your design needs.  It is also the cheapest weight to use.

Tungsten is more dense than lead and is safer to handle but is more expensive and not very willing to have its shape changed.  It is available in cylinders and is an excellent choice if it fits your design parameters and wallet.

In addition, there are a number of supplemental weights that you will need in order to truly maximize the 5.0 ounce limit!
 

Graphite is by far the most common lubricant for pinewood derby and becomes your only good choice if the rules require dry lubricant.  Graphite with molybdenum is the most common, but Tube-O-Lube is gaining some market share.  Tube-O-Lube provides somewhat slower spin times but is considered a slightly better lubricant under load with the wheels pressing against the axle going down the track. 

Teflon lubricant was expected to take the pinewood derby by force, but has really fallen on its face.  Simply put, don't even think about it past the end of this sentence.