Dough too dry — stiff, cracking, and refusing to come together

What is causing it

Flour measured by volume. A cup of flour can vary by a third depending on how it was scooped. This is the single commonest cause and it is why bread recipes are written by weight.
A thirstier flour than the recipe assumed. Wholemeal, rye, spelt and strong bread flour all absorb more water than plain white. A recipe written for one and made with another comes out dry.
Dry conditions. Flour picks up and loses moisture from the air. The same recipe genuinely needs more water in a dry heated kitchen in winter.
Not enough resting. Flour takes time to absorb water. A dough that feels dry two minutes after mixing often feels correct twenty minutes later.
Too much extra flour during kneading. Dusting heavily to stop sticking works the dough progressively drier without anybody deciding to.

Add water carefully — a dough that has gone too wet is harder to correct than one that is slightly dry.

First, stop and wait. Cover the dough and leave it twenty minutes. Flour hydrates slowly and a great many "dry" doughs are simply young.
If it is still stiff, wet your hands rather than pouring water in. Knead with damp hands and repeat. This adds water gradually and evenly.
For a larger correction, add water a tablespoon at a time, working it fully in before adding more. It will look like it is not incorporating; keep going.
Expect it to go through an unpleasant sloppy stage before it comes back together. That is normal.
Stop while the dough is still slightly firmer than you want. It softens as it proves.
Once shaped, do not add anything further. Water worked into a shaped loaf destroys the structure.

Weigh everything: Flour and water both, on scales. This removes the commonest cause outright.
Hold back some water: Add roughly nine tenths of the water, mix, then decide. Adding is easy; removing is not.
Autolyse: Mix flour and water only, and leave it twenty to thirty minutes before adding salt and yeast. The dough hydrates fully and needs far less kneading.
Match the flour: If a recipe says strong white and you have wholemeal, expect to add roughly a tenth more water.
Dust lightly: Use oil on the worktop rather than flour for wet doughs, or a scraper instead of more flour.

Useful for confirming the diagnosis after the fact.

A tight, close crumb with small even holes rather than an open irregular one.
A pale crust, because there is less moisture to carry heat and less steam to delay setting.
Poor oven spring — the loaf barely rises once it goes in.
A loaf that stales quickly, because it started with less water than it should have had.
Tearing along the shaping seams, where the dry surface could not stretch.

Yes, with damp hands or a tablespoon at a time, worked fully in. Not once the dough is shaped.

Flour holds moisture from the air. A dry heated kitchen genuinely changes how much water a dough needs.

Softer and stickier than most people expect. A well-hydrated dough is slightly tacky and slack rather than smooth and firm.

No. Kneading will not add water and it will tighten the gluten further. Hydrate it first.

Rarely. Corrected early it bakes normally; corrected late it makes a dense but perfectly edible loaf.