I have a BTwin Triban 3 which has a triple chainset that needs replacing. I am thinking of replacing it with a double chainset this time. Is this possible, or do I need new shifters and a different rear cassette? Could someone please link me to a good tutorial that will show me how to replace the chainset.
You'll need a new bottom bracket with a different axle length, a new crankset of course, front derailleur and matching shifter. Since you'll probably need to buy a complete set of brifters it will be quite an expense. And while you're at it you'll probably have to get new cable housings and cables for the brakes. Not to mention new bar tape. At least you can keep the rear derailleur and the cassette if the resulting new gears suit you, but you may need a new chain.
And if your triple has less than 10 gears on the cassette you'll probably have to find an older double crankset and matching shifters.
INMHO I would keep the bike as it is because the expense will be quite hefty.
First, are you really sure the crankset needs replacing? Maybe you just need new chainrings. It takes a lot of riding to wear out a crankset, like 10000 kilometers at least. If you've done enough riding to wear out a crankset, you will likely need to replace the rear cassette and chain at the same time. If you are maintaining the bike at all, you should get at least 4 or 5 chains and one rear cassette replacement before you need to even look at replacing the front chainrings. Even a low end bottom bracket should last 20-30K km's, and the cranks themselves should last nearly the life of the bicycle.
What problem are you having that makes you think you need to replace the entire crankset?
If you really do need a new crankset, or just want different gears, it's quite possible that all you would need to replace is the crankset. However, it's not guaranteed to work, you are attempting to do something that is not in the manufacturers recommended use. Often this works out just fine since bicycles are pretty forgiving machines, much depends on how tolerant you are of slightly imperfect or slow shifting.
There are two good sites for learning to work on your own bike.
Exactly what you'll need to replace will depend what new gears you choose. The key measurements are the chainline of the new crankset and the size of the small and large chainrings and the clearance of the derailleur. A triple derailleur often has a shape that will not work well with double chainring.
Bicycles are very tolerant machines and you can do a lot of bodging to make things work that are not guaranteed to work out of the box. However, converting a triple to a double is not a good introductory project. There have been a lot of changes in bottom brackets, cranksets and shifters in the last 10 years and exactly what works with what can be quite tricky.