The goal here is a plane that takes a full-width shaving, achieved without removing anything you cannot put back. Every step below is ordered so that the reversible work happens first and you get a chance to reassess before doing anything permanent.

Before you start: date the plane. If it turns out to be an early type, an unusual variant, or unusually complete, stop and reconsider. Aggressive cleaning takes a large and permanent bite out of the value of a scarce tool. The dating guide takes five minutes and can save you several hundred dollars of regret.

1. Dismantle and photograph

Take it apart completely: lever cap, iron and chipbreaker, frog screws, frog, knob, tote, depth adjuster, lateral lever if it comes off.

Photograph it before and during. You will not remember which way the chipbreaker screw faced or how far the frog sat back.

Put the small parts in a jar. Frog screws in particular are a specific length, and finding a replacement that seats correctly is more annoying than it sounds.

2. Assess before you clean

With everything apart, check the four things that decide whether the plane is worth the afternoon:

Cracks. Look at the mouth, the cheeks, the tote boss and around the knob seat in raking light. A cracked casting is not worth restoring unless the plane is scarce.
The sole. Sight along it. Gentle wear is fine. Visible twist is a long job.
The mouth. A mouth that has been filed open cannot be closed again on a Bailey except by moving the frog forward, which limits how fine a cut you can take.
The iron. Measure the usable steel above the bevel. Under about an inch and a half and it is nearly used up.

3. De-rust

For light surface rust, a green abrasive pad and a light oil, worked by hand, is enough and takes off nothing but rust.

For heavier rust, an overnight soak in a rust-converting solution or a citric acid bath (a heaped tablespoon per litre of warm water) does the work chemically without abrading the surface. Rinse thoroughly, dry immediately and oil at once — freshly de-rusted iron flash-rusts within minutes.

Do not put a japanned casting on a wire wheel. It will strip the japanning in seconds, and japanning is both part of the tool's value and hard to replace convincingly. Keep the wheel for the sole and the sides if you use it at all.

Brass parts — the depth nut, sometimes the lever cap screw — clean up with a soft brass brush. Resist polishing them to a mirror; nothing signals an over-restored plane faster.

4. Flatten the sole

Only if it needs it. Many planes cut perfectly well with a sole that is not dead flat.

Work on a known-flat reference: a machinist's plate, thick float glass, or the wing of a decent table saw. Put wet-and-dry abrasive down — 120 grit to start, then 220, then 320 — and work the plane along it with the iron installed and tensioned but retracted, because clamping the lever cap stresses the casting and changes its shape slightly.

Mark the sole with a permanent marker first. When the marker is gone from the toe, the heel, and both sides of the mouth, stop. Those are the areas that must be coplanar; the middle of the sole does no work.

Check your progress often. It is very easy to keep going and round the toe over.

5. Handles

Rosewood knobs and totes usually just need the grime taken off and a wipe of oil. Do not sand a tote that has a hundred years of hand-polish on it.

A cracked tote — almost always at the horn — repairs well with thin cyanoacrylate or hide glue, clamped. A tote that has broken clean through can be glued and will hold fine for normal use.

If the finish is truly gone, a few coats of shellac or a wiping varnish is period-appropriate and easy to renew later.

6. Sharpen

This is the step that determines whether the plane works, and the one people skimp on after doing everything else properly.

Flatten the back of the iron for the first inch. Coarse stone or abrasive on glass, then progressively finer, until the last inch is uniformly polished. Do this once properly and never again.
Grind the bevel to 25 degrees if it is chipped or badly out of square. A honing guide is not cheating.
Hone a secondary bevel at 30 degrees through your finest stone.
Strop or take off the wire edge on the finest stone.

The edge should catch on a thumbnail with no pressure and shave hair off your arm. Anything less and the plane will disappoint you no matter how flat the sole is.

Fit the chipbreaker so it meets the back of the iron with no gap — hold it up to a light. A gap means shavings jam under it, and a jammed plane feels like a blunt one.

7. Reassemble and set

Frog back on, screws snug but not tight.
Iron and chipbreaker in, lever cap on, cam closed with firm resistance — if you need force, the lever cap screw is too tight.
Sight down the sole from the toe and advance the iron until it just appears.
Square it with the lateral lever until the edge is parallel to the mouth.
Back the iron off, then advance it slowly until it takes a shaving.

Set the mouth by moving the frog: forward for a tighter mouth and finer work, back for heavier cuts.

8. Test on real wood

Take a shaving off a piece of straight-grained softwood first, then something harder. A tuned plane should produce a continuous full-width shaving you can read a newspaper through.

If it chatters, check the lever cap tension and that the frog is fully seated. If it tears out, close the mouth and reduce the depth. If it will not cut at all, it is not sharp — go back to step 6, however sure you are.

What to skip

Repainting or re-japanning. Unless the casting is bare metal, leave the finish. Amateur repaints look amateur, take value off, and do nothing for performance.

Polishing every surface. A mirror-finished plane is somebody's hobby, not a better tool.

Replacing original parts with modern ones on anything scarce. A thick aftermarket iron makes a common user plane cut better and makes a collectable one worth less. Decide which you have before you order parts.

Sources

reference-site
Patrick Leach's Blood & Gore (Stanley plane model-by-model commentary) — Patrick Leach
book
Dictionary of American Hand Tools — Alvin Sellens

Restoring a Stanley Bailey Plane, Step by Step