You can't stain a steel door, of course, because steel isn't porous enough to stain, but you can use gel stain to make the door look like wood. It's a proven technique that delivers spectacular results if you do it right, and that isn't as challenging as you might expect.
The two secrets to a top-notch job are to first paint the door with a color slightly lighter than your chosen stain color and to use a cheap paintbrush to apply the gel stain. The reason you want a cheap paintbrush is that it's more likely to leave brushstroke marks, and that's what makes the stain look like it has a grain. You can go one step further and use a wood graining tool, which is fine, but it isn't really necessary. You can get great results without it.
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Prep and Paint the Door
Get the door ready for painting by removing the doorknob, deadbolt lock, and any other hardware that might get in the way. If the door has a window, mask off the glass completely with masking tape so you can work freely without worrying about getting paint or stain on it. Finally, give the door a good cleaning using soap and water or isopropyl alcohol and let it dry.
The best paint for the undercoat is satin acrylic enamel with a color slightly lighter than the stain. Apply it with a good-quality paintbrush (not the brush you use for staining) and paint the door in sections. Brushstroke direction matters because it helps enhance the faux-wood effect. Use vertical strokes on the stiles and panels and horizontal strokes on the rails. It's good to complete all the sections that require vertical strokes and then go back and do the horizontal ones or vice versa.
Apply the First Stain Coat
You'll need a large collection of rags because the staining procedure involves painting on the stain and then wiping off the excess, leaving just enough to cover the paint. Work in small sections to avoid having the stain dry completely before you wipe it off.
Brushstroke direction matters even more when you're applying the stain, so use horizontal strokes anywhere you painted with horizontal strokes and vertical strokes elsewhere. To avoid having the strokes overlap at places where they change direction, lay masking tape on the edges of all horizontal sections and then paint the vertical ones. Let the stain dry for an hour or two and then remove the tape, lay fresh tape on the edges of the vertical sections, and stain the horizontal ones.
Apply a Second Coat and Then Polyurethane
Let the first stain coat dry overnight (eight to 12 hours) and then apply a second coat in the same way you applied the first. If you're going to use a graining tool, now is the time to do it before the second coat of stain dries completely. Depending on the look you're after, you may decide on a third coat, and if so, use the graining tool on both the second and third coats for the best effect.
Give the final coat eight to 12 hours to dry and then cover it with one or two coats of clear polyurethane. A water-based product is preferable; it dries clear and won't affect the faux-wood appearance of the stain, and it dries quickly, so you can apply two or three coats in a single day. Brushstroke direction still matters even when you're applying a clear finish (for which you should use a quality paintbrush, not a cheap one). Always brush with the direction of the faux wood grain.