All ingredients are poisons: keep away from children.

Notes such as (A) expand details, alternates, and WARNINGS. Another list tells where to buy materials.

These instructions may be freely copied and circulated as long as credit is given and no profit is made.
 

Supplies

screwdriver
wooden match
teakettle of BOILING water
cleaning solvent (A)
hydrogen peroxide
tow (raw flax)
ramrod and worm OR cleaning rod (D)
small toothbrush
rags
nylon scrubbie
steel wool
olive oil
boiled linseed oil
neat's foot oil or mink oil
detergent
rubbing alcohol
 

Steps

1. Partly dismantle.
Remove lock, screws, flint, jaw leather, doghead, ramrod. Swing down flashguard. Gently scrape off coking. Whittle match, insert in touchhole. (B)

2. Flush.
Pour a shot of hydrogen peroxide (C), then boiling water down the barrel. (Hang onto the sling. The barrel gets hot!) Shake and pour, repeat. Twirl tow on worm (D), soak with solvent, swab barrel. Flush. Pull match, flush touchhole. Flush lock and parts.

3. Scrub with solvent.
Scrub gun with toothbrush and nylon scrubbie soaked in solvent. Wipe dry and prop gun upside-down. Scrub lock and parts, flush with hot water, dry. Steel will be stained but clean. Let all parts air-dry. (E)

4. Treat wood.
Sand out dings with steel wool. Rub linseed oil into wood using your thumb, especially around lock. Let stand a while (one hour max), then wipe off excess. (F) With a Bess, check pins and plug ends with beeswax.

5. Treat leather.
Rub leather sling lightly with neat's foot oil or mink oil. (G)

6. Oil metal.
Swab inside of barrel with oiled tow once. (H) Wipe all steel lightly with olive oil. (I) Too much oil just collects dust and bugs.

7. Reassemble gun.
Reassemble except for flint and jaw leather. Drip oil inside lock. Wash hands with detergent.

8. Store musket.
Always carry musket in case or blanket to avoid spreading oil and catching dings and rust. At home, IMMEDIATELY uncase and hang musket on pegs or stand in corner, out in open air. NEVER keep in a closet or case, else it will rust. Uncock trigger and tilt frizzen forward to relax springs. Wipe with oily rag once a month and after handling.

9. Prep before shooting.
Wipe frizzen, flint, and pan with rubbing alcohol to remove oil. Swab barrel with clean tow to remove oil and obstructions.  Click for instructions How to Install and Sharpen a Musket Flint.
 

10. Clean at end of season.
Completely dismantle and polish all parts. (J) Treat wood. Clean strap with saddle soap or mild detergent.

Notes

(A) Cleaning solvent is one-third Murphy's Oil Soap, one-third rubbing alcohol, and one-third hydrogen peroxide. WARNING: this solution generates a volatile gas. Do NOT seal in a tight bottle: it may explode. Either a) make up just a batch for cleaning, then discard remainder, or b) put in a bottle with a loose cork (which can be pushed free by the gas buildup) or poke a hole in the bottle cap. Little green bottles from any Dollar Store make good containers and look period: buy new corks from a hardware store.

(B) A double-ended angle screwdriver (hardware store) is small and easy to grasp with oily hands.

(C) Hydrogen peroxide eats steel, but it's the only way to dissolve the black guck. Flush well with boiling water.

(D) Instead of a ramrod, make a cleaning rod from a 4' 1/2-inch dowel and a packet of brass curtain hooks (hardware store). Screw a hook into either end. Mash one into an almost-closed loop for the tow. Cut and square the other hook into a flat-ended scraper to scrape the bottom of the barrel. Store the rod in the gun case alongside the gun.

(E) Alternate methods of scrubbing. Use wintergreen oil and a nylon scrubbie. For a real period method, dip a rag in neat's foot oil, then dab into brick dust, and scrub.

(F) WARNING. Rags soaked in linseed oil can spontaneously combust. (The notorious "oily rags" that start fires in news reports.) Wash the rags in detergent and discard.

Volumes have been written on wood oils, the never-ending argument. I prefer linseed oil: it looks good, is period, lasts long, makes a tough plastic coating that will fend off dings and scratches, is cheap and easy to apply. Alternatives abound. Tung oil looks great but is tricky to apply and may irritate your skin. Lemon oil looks beautiful on a Bess but evaporates in a day or two. Butcher's wax also works. Gun oil and Bore Butter are NOT good for wood.
 

(G) Use neat's foot oil or mink oil sparingly. A little revives leather remarkably. Too much makes leather squishy and limp. Rub in with a rag and let dry.

(H) To reuse tow, tie it insiden an old stocking and wash in machine.

(I) Discussions about gun oils for metal are endless. 18th century people used neat's foot oil, but it must be applied daily else it evaporates in a few days. Some might have used whale oil, tallow, or whatever grease/oil was handy. Nowadays some experts use any salad oil: canola, corn, etc. I prefer olive oil, which is tough, doesn't evaporate or turn rancid, washes out of clothes easily, and protects steel even in drizzle. Disadvantage: left too long, olive oil oxidizes to a brown crust, but this continues to protect the gun and comes off easily with cleaning solvent. One guy wipes his gun with Baby Wipes containing lanolin (grease pressed from sheep's wool). Modern gun oils work, but some experts think petroleum products harm antique and replica guns. Your choice.

(J) Completely dismantling is a major project. Lay the parts out on a flat trash bag IN ORDER to remember where they go. Better, just dismantle one section at a time. Alternatively, as you pull parts off, lay them in a large flat tupperware container soaking in turpentine. Scrub steel on a wire or buffing wheel. Put a box over the parts so the cat doesn't bat the screws around. 
 

Where to Buy Materials

Hydrogen peroxide. Drug store or grocery store.
 

Rubbing alcohol. Drug store or grocery store. Get the 90% solution, not 70%.
 

Murphy's Oil Soap. Grocery store.
 

Tow. Raw flax, plant fibers spun to make linen. Handier than rags. James Townsend & Sons.
 

Boiled linseed oil. Gun shop or hardware store.
 

Neat's foot oil, boiled from cow's hooves.  Getting hard to find.  Try a sporting goods shop (used to soften baseball gloves) or hunting supplies store (used to waterproof boots).  Or substitute mink oil.  Kiwi's brand is sold in most grocery and department stores in the shoe care section.
 

Olive oil. Grocery store.
 

Lemon oil. Grocery store.
 

Wintergreen oil. Special order from druggist or try a health store.
 

Brick dust. Smash up an old brick. Purists use only 18th century bricks.
 

Nylon scrubbie. Grocery store.