Somewhere along the way someone has come up with the notion that you should seal the wood before you stain. Don't seal first. If you seal the wood first there is nothing for the stain to soak into and the it sits on top of the sealer and looks very blotchy
Sealing after staining is a good idea as some pigments will bleed through a finish and give an undesirable appearance, so it is a good idea to seal them in. Besides when you use a sanding sealer before you apply the final finish you can sand it with a very fine sandpaper to give a very good, very smooth surface on which to apply the final finish.
Be sure that you use a sanding sealer compatible with the other products that you are using especially with the final finish product
Staining wood furniture is generally a necessity after you strip and prepare it. If you don't, the piece of furniture will quite often look uneven in color or kind of blotchy. An exception to this is a clear finish over light color wood that you want to have a natural appearance.
You can get products that are a combined pigment and finish that dry quickly (other than the pigmented oil finishes), but they will generally give a muddy opaque finish.
There are vinyl or aniline stains, and many more that are quick to dry, but are usually very difficult to use or just plain frustrating, because they dry before you can get the effect that you want. It's just like most things in this life, if you want fast, then you have to give up some other quality.There are pigmented oil finishes, that generally give good color. Watco Danish Oil is a good example. It will be covered more in Wood Finishes.
My favorite is a good oil stain, they give you lots of control. Always pick a color no darker than you want the furniture to be. If the furniture is too light you can always apply more stain and let it penetrate longer, but it is a lot of work and sometimes the result isn't what you want if you have to lighten the furniture. If the color you want is in between the colors available, you can mix oil stains to get your desired color.
Oil stain can be applied with a brush, cloth, roller, your bare hand, or by any other means as long as you get it on evenly. After applying, wipe the excess off and let the furniture dry overnight. It is very important that the stain is completely dry before applying a clear finish.
See Finish Wood Furniture for the next step after the stain dries.