If you truly need to remain completely anonymous and untraceable then you need to completely eliminate any connection to your real identity.
* Make up a fake identity. (name, address, birthdates, etc.)
* Get a prepaid cell phone (for verifying accounts)
* Get a prepaid credit card. (for verifying accounts and doing financial transactions)
* Get a laptop exclusively for your untraceable business, set it up using only your fake identity information,
* DO NOT ever enter your real name into any program or enter real data on any websites while using that pc.
* Load it with any programs you need for your business, only use your fake identity to register those programs.
* Again - Never put any of your real contact info on it!!
* When you need to be anonymous use only the computer, identity, cell phone and credit card you set up.
* Never use your own internet connection to connect to any of your online business, only go online at publicly available wifi hotspots. (libraries, internet cafes, public wifi systems, etc.) Even better if they aren't in your local neighborhood.
* You can also find unsecure home networks to connect to, if you do that it's best not to use your neighbors. You want to leave your neighborhood and drive around till you find a wireless connection you can log on to.
* If you set up an online businesses and plan to deal with large amounts of money then you probably will also need to find an online bank to set up an account for the fake identity. Also set up paypal account for the fake identity linked to the credit card and bank accounts. That isn't always the easiest thing to do, but it's possible if you do some research.
* Make sure that absolutely nothing you do has any connection to your real identity.the only way to get money is cash withdrawals using the credit card. Never do any money transfers for or to accounts in your real name.
The last thing is -
* If you do any withdrawals at an ATM location, bank or store with a surveillance cameras they could have a photo to identify you with. (Same thing could apply to a lesser degree at the places you go to connect.) If it's that important then you need to do some research and make sure the places you use don't have video cameras.
It would be a lot of work, but if you did all that you could conduct online activities without any possibility of tracing it back to you.