If you own an air compressor, especially an inexpensive one, chances are that you'll encounter a blown head gasket at some point.

Symptoms include

Compressor runs without stopping, but never reaches pressure
Air can be heard or felt escaping (hissing) between the compressor head and the main compressor body casting
Compressor head becomes much hotter than under usual operation

The cylinder head gasket seals the gap between the main compressor body casting and the cylinder head, similar to a head gasket in a car engine. On many smaller compressor models, there can be very thin sections of the gasket that may be pushed out of place and leak or tear out completely, preventing the compressor from, well, compressing.

Fortunately, this is a relatively simple problem to fix using basic tools and inexpensive parts that can be found at any auto parts store!

(example compressor image used under CC/SA license from Leeds Hackspace, https://wiki.leedshackspace.org.uk/wiki/Air_Compressor)

Supplies

Materials

"Karropak" gasket material - This is a chemical-impregnated felt paper, usually sold in 1/64", 1/32", and 1/16" thicknesses in the US. The. paper is treated with gelatin and other chemicals to make it durable, oil/gasoline-resistant, and heat-tolerant. It can be bought in sheets or rolls in most auto parts stores. Manufacturers include Fel-Pro in the US and Jointine in the UK
Gasket Sealant Adhesive - A viscous glue designed for high-temperature and oil resistance that is similar in consistency to rubber cement. Many brands are dyed red and include an applicator brush in the container. This stuff is stringy and sticky - wear gloves!

Tools

Craft knife (e.g., X-Acto)
Small disposable brush (if sealant does not have a brush)
Latex or nitrile gloves
Cutting surface (e.g., scrap wood)
Hex ratchet set (may need an extender, depending on your compressor)
Screwdriver (as needed for disassembly of the compressor)

Step 1: Disassemble Compressor Head

The main body of the compressor is usually two parts, a main body casting, and a cylinder head casting. On some compressors, there may be more than one cylinder head. Disassembly will vary a bit depending on your compressor, but generally, the process is similar to this:

Unplug the compressor
Release pressure from the compressor (usually using the petcock at the base of the tank)
WAIT FOR THE CYLINDER HEAD TO COOL! It can be hot enough to case injury, especially if the compressor has been running for a long time.
Remove the shroud to expose the compressor head. There are usually two or more screws holding the shroud in place. On some compressors, you may beed to remove an air filter or handle to remove the shroud.
Remove the bolts holding the cylinder head in place. In this fairly typical example, there are four hex bolts recessed into the top of the head.
Remove the cylinder head casting. The gasket may stick to either the top or bottom casting, and may tear if especially well-stuck or severely damaged. BE CAREFUL to keep any loose pieces of gasket material (or anything else) from falling into the cylinder. Bits of debris can permanently damage the cylinder if nor removed before running the machine!

(Parts diagram from user manual for Harbor Freight Model 40400 shared here under fair use)

Step 2: Clean the Mating Surfaces

The smooth faces of the compressor body and cylinder head will likely have sealant/adhesive stuck to the surface, and it may be burned to a VERY persistent tarry mess.

Working outdoors, with plenty of space for airflow, use a cleaning solvent to remove all the remaining residue. Gasket sealant/adhesive is designed to resist petroleum distillates, so you'll need something like lacquer thinner (usually acetone) or Goof-Off (contains xylene) to remove it.

Allow the surface to dry completely.

Step 3: Rough Cut the Gasket

Cut a piece of the gasket material to fit the mating surface. The piece should be just slightly larger than the surface (e.g., extend 1mm past the edge on all sides).

Step 4: Trace the Gasket and Cut to Fit

If the original gasket is in good enough shape, you may be able to trace it directly onto the new gasket material. However, in many cases, the gasket will be too deformed from the blowout to work as a good template.

You can press the new gasket material against one of the mating surfaces to leave enough of an impression or print to trace (see image). Go over the faint lines with a pencil if needed.

Cut out the gasket and dry fit it against the casting to check fit.

Step 5: Apply Gasket Sealant/Adhesive

Apply gasket adhesive according to the instructions. In most cases, this will mean:

Apply sealant to both metal mating surfaces
Apply sealant to both sides of the new gasket
Allow sealant to dry to slightly tacky (usually only a minute or less)

NOTE: This stuff is MESSY and STICKY! Wear gloves and make sure you have a plan for where to put whatever ends up covered with goo!

Step 6: Reassemble Compressor Cylinder Head

Place the now-tacky gasket on the mating surface of the main casting
Replace the cylinder head carefully over the new gasket
Insert and tighten the bolts holding the head in place. DO NOT OVERTIGHTEN. Overtightening can strip the threads in the casting, which would need to be a whole other 'ible to repair
Replace the shroud and reattach with the original screws