You can stain MDF but it needs a little preparation first...
If you seal it first, after sanding with 320 grit paper, with a propriatory MDF clear sealer...or ordinary sanding sealer, the type that won't colour it, and then stain it, you'll find the finish is much better. Sanding lightly with the used 320 paper once again before you stain.
You can apply the stain with a brush to achieve some kind of "grain" effect but you're better applying the varnish with a synthetic roller for a good finish. A water based laquer seems to give the best finish in my experience.
And don't forget to seal all the edges very well or you can get "break-out" on the edges if there's any humidty/damp.
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