How do I stain/paint Ikea birch Wardrobe pieces ebony?
If you're feeling adventurous you could try spraying on a tinted top coat, that way you could achieve the ebony(ish) color and preserve the grain pattern. Its a tricky technique and it must be sprayed but it can be done. 

There are a few variations but in general you add 10-20% dye stain to a finish like urethane or lacquer and spray on enough coats to get the color saturation you're after. Prep the surface as described by Steven and then apply an un-tinted clear sealer coat (my personal preference is Zinser's shellac based sealer). Sand with 280 and then add two coats of your tinted top coat, spraying in different directions (left to right then up to down). If it requires more coats, sand with 320-400 and continue on, sanding every few coats. If you have to let it sit for an extended period between coats (more than a day) be sure to sand to promote adhesion.