It's really simple to change your electricity or gas company. Just call your chosen supplier (or apply online on their website). At this point, it's a really good idea to have a record of your last 12 months' energy use - you can get this from your existing supplier or bills. You can then use this information to check out the different products / deals available from your chosen supplier.
Once you've agreed your new contract, you'll receive a letter from your new supplier within 7 working days confirming all the details. You won't need to contact your current supplier as your new one will do this for you.
You'll need to give your new supplier a meter reading - this is really important as the correct reading will make sure you're billed for the right amount - and from the right time! Your new supplier will then give your old supplier this meter reading.
The whole process shouldn't take more than 6 - 8 weeks to complete. Please remember - don't stop your payments to your current supplier until you've paid their final bill - they could object to your transfer if you owe them money.
The whole process should also be trouble free but if at any point, you have any concerns, just speak to your new or old supplier and they'll work together to resolve any problem quickly.
If anyone is unsure who to transfer to, I'd recommend checking out the deals and products online at www.uswitch.co.uk.