You've got the first step right - raise the grain with water and then sand
The dyes will dye the oak just fine, but you may want to mix it a little
darker to start. Mix it dark, do a sample on a piece of scrap oak. If it
is too dark, you can lighten the stain by adding a little water to the mix.
If you stain your project a little too dark, you can lighten it somewhat by
wiping the surface with a wet rag. However, repeated applications of dye
won't really darken further.
Remember, with dye stain, you are actually dyeing the wood just as you would
dye cloth; the dye goes into the fibers of the wood, and you don't want dye
just sitting on the surface.
When you apply the dye, you want to flood the surface of the wood, let it
soak in good, then wipe off the excess.
The liquid dye stain you purchased is very good for tinting water-based
lacquer. Roughly 300 drops per quart, iirc, varying with how dark you want
the tint. Lightly tinted lacquer can give a real nice luminous color
effect, and more tint in the lacquer can help mask dissimilar wood colors.
That's all I can think of for now, as I've only had half a cup this morning.
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