A typical firearms examination concerns matching a bullet back to the gun that fired it, to the exclusion of all others.  

Bullet Matching.

Certain parts of a firearm mark the bullet and cartridge.  Rifling gives the bullet a signature marking that is unique to the weapon that fired it.  Rifling exists as part of the manufacturing process of the firearm and serves to put spin on the bullet, giving it a straighter trajectory (much the same way a quarterback puts spin on a football).  Rifling consists of lands and groves that spiral down the gun barrel (think of the seam on a paper towel tube).  When the gunpowder in the cartridge is ignited, it forces the bullet down the gun barrel, expanding the soft lead into the lands and groves.  As the bullet passes down the barrel, microscopic scratches from the lands and grooves mark the bullet.  These microscopic scratches are a by-product of the manufacturing process and are totally unique to a particular firearm.  Thus, the scratch marks on the bullet match the scratch marks in the barrel of the gun that fired it, to the exclusion of all other weapons.  

This is tested in the lab by test firing a bullet through the suspect weapon.  The test fired bullet is then compared under a comparison microscope, side by side, to the bullet recovered from the crime scene.  Both bullets are rotated until the striations can be made to line up, showing a match.  If the striations cannot be lined up, the result is negative.

Imprint Evidence.

There are two basic types of imprint evidence:  Three dimensional impressions, in which an object presses into something soft which retains the impression of that object; and two dimensional impressions, in which an object transfers an image to a surface or an object comes into contact with a surface that is coated and removes some of that coating.  

An example of a 3d impression is something stepping into mud.  You've all seen Big Foot documentaries where a camper finds a huge foot print out in the woods.  This is a 3d print.  Big Foot (for lack of a better explanation) has stepped in the mud and left a foot print behind. The mud hardens as it dries and retains the print.

An example of the first type of 2d print would be the step after you've stepped into spilled paint.  The paint coats the bottom of your shoe when you step in it.  It is then transferred to another surface when you step down.  It is just like using a rubber ink stamp.  

An example of the second type of 2d imprint is when you stepped into the paint.  You removed some of the paint, creating a negative image of the bottom of your shoe in the paint spill.

Impression evidence can be so detailed, to the microscopic level, that it can be used to identify both class and individual characteristics.  Not just used for shoes, impression evidence can also be used with tire impressions (a tire impression is just like a long, continuous shoe impression) and tool marks.

Tire impressions can be extremely useful.  Let's say there is a bank robbery.  The perpetrators parked behind the bank.  As the fled, they unknowingly left behind a bunch of clues.  

Wheel base is the distance between the two front wheels and the distance between the front and rear wheels.  There are guys in labs who have charted out these distances and can use this chart to narrow down the make of the car.  The tread design itself, as discussed above, can narrow down the list of possible cars.  There are books that contain images of every type of tire imprint, just for this purpose.  The individual wear developed from use will show up in the impression, allowing for identification of a single car, to the exclusion of all others. We can also tell which way the car was facing, how they pulled out and in what direction.  

Tool Mark Evidence.

There are three types of tool mark impressions: Compression, in which a tool surface presses into a softer material; Sliding, in which a tool  (such as a screwdriver) scrapes across a surface causing parallel striations; and cutting, which is a combination of the above two types (as with scissors).  All three types can yield class and individual characteristics.  In this way, marks left on a doorway from a pry bar can be matched back to that specific pry bar.

Explosives.

Without getting too into it, explosives residue can be analysed to determine the type of explosive used in a particular detonation.  Also, some manufacturers are now putting chemical tags in their explosives that will allow for tracking of specific batches by chemical composition or other tangents.

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