This can vary depending on the type of dye being applied (water-based or solvent-based) but this stands as good general advice. Always read the manufacturers guidance on the product tin / container.
Mix the wood dye thoroughly before and periodically during use.
Best applied using a synthetic bristle brush, sponge, foam applicator or spray gun. A foam sponge is highly recommended when working on large flat pieces, as any heavily stained areas can be soaked up by the sponge as you work. Similarly by applying a little more pressure, more of the wood dye can be released to save time returning to the container for more.
Apply a generous coat in the direction of the wood grain leaving a little on the surface and wipe off any excess dye as you go with a clean, lint-free cloth. Allow the dye to fully dry.
Denib (lightly sand) using a fine finishing pad to loosen and remove any dry, powdery dye residue from the wood surface. Take care to remove all traces of dust with a vacuum cleaner or clean, dry microfibre cloth before sealing the dye with a suitable top coat.