OK this might not be very clear in words but here goes:
First you need brushes NOT those sponge applicator thingies. Now this might seem obvious to many but for me it was a total revelation.
You want a colour not too far from your skin tone as a 'transition' colour to put on first. This will make everything else blend nicely. Put a tiny bit on at the outer corner of your crease (your eye socket) with a blending brush and then do a windscreen wiper motion back and forth across your whole crease to blend. If you can barely see it, put a bit more on, but build it up.
Then go for a slightly darker colour in your crease, either with the same brush or a slightly smaller brush and do a similar motion, again build it up. Blend blend blend, and then blend a bit more.
Then a darker colour again in your 'outer v' (the v shaped bit at the side of your socket/eyelid, a Google will show you). And again blend.
Different looks require different things but this is the basics for a nice blended eyeshadow look with a bit of depth and takes no time at all really. Also you can put a bit of lighter coloured more shimmery stuff on your lid with a dense brush or your finger. Try not to put much shimmer in your crease (ahem) as if you are older than about 20 it just creases up and also doesn't create the dimension that mattes do.
As for colours, I am a believer in anything goes, and you can't really go wrong with browns and taupes, but officially going by the colour wheel the colours that would make your eyes pop the most would be purples and pinks.
The ABH modern renaissance palette would probably be great for green eyes but it is £££.