If you use concealer/foundation/powder/blusher etc then apply all that first. I always prefer to do my eyes last but if you tend to be messy with your eye make-up then do them first, clean up any smudges then do your base.
You will need two or three eyeshadows, preferably they should be shades of the same colour (good ones for smokey eye are black, grey, brown and dark purple). You will also need a natural coloured eyeshadow for the base coat.
Start by apply the natural colour over your entire eyelid, but don't be tempted to go right up to your eyebrows. If you prefer you can use an eyeshadow base instead, but I like to use shadow.
Next apply your first colour. For best results use your lightest shade first (but obviously not the one you used for your base coat). Apply it over your lid and just above the crease (this is where the top of your eyeball ends and sits in the eye socket). Don't worry if it looks messy because you can sort that out and blend it later on.
Take your next shade of eyeshadow (it doesn't matter which one, it can work with the darkest and medium shade) and apply it into your crease. This is where you need to start blending. You can use either a soft eyeshadow brush or your fingers to do this. With either the brush or your finger, smooth out the two colours so that they blend into each other and there are no harsh lines. Don't be tempted to over blend though, the darker colour still needs to look darker.
Now we need to do the eyeliner. Some people like to use pencil on it's own and some use just shadow. Shadow does stay on longer and looks better with this look, but it's up to you, you might like to use both. If you're using eyeliner, apply it straight to your lower waterline. If you want to add shadow, then take a thin eyeshadow brush, load it with colour and gently run it underneath your eye. It doesn't matter about neatness because we're going to smudge it slightly to give that 'smokey' effect. Preferably a specialised smudging brush is best for this, but any soft thin eyeshadow brush will do. Take the brush and gently blend the shadow out and into the liner so that it looks smudged and sultry. This is also the point where you should apply liquid eyeliner if you want to, apply it only to the top lid and feel free to add a small flick at the corners if you want. However this step is optional and takes a lot of practice to get right.
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