The Tournament of Champions is unlocked after earning 200 ToC points, assigned by your placement in other events. It will unlock after taking 1st place in all four events at Grand Casino Tunica, the first venue, then 1st in the first event at Harrah's Rincon San Diego, the second venue.
The basic strategy that I followed in order to win every event, including the ToC, was as follows:
First of all, take advantage of the autosave feature. Whenever you have won a big pot, press start to force the game to autosave your current progress in the event. When you lose a big pot or bust, sign out of your profile via the Guide, returning you to the main menu, then sign back in again and reload your Career, resuming where you last saved in the tournament. Installing the game to your hard drive will save you even more time, as you will likely be doing this quite a few times over the course of your career. (credit to Duke x360a and TastyPastry for this method)
In regards to the actual events, the most expedient method I found was to wait until you have a good hand (not necessarily a premium one - any pocket pair or AK - AJ will basically work), and go all-in. If you double up, great, if not, reload. Repeat this a couple times until you have a very clear chip lead. At this point, fold everything but premium hands so that the field thins out and you reach the final table quickly. Do not bother actually playing poker, just shove good hands and go for coin flips. Once you have a huge stack, you will more often than not have your opponents fold even when they have committed most of their stack to the pot (the AI is not very good). Thus, even though your opponent will sometimes win against your shove, you will still profit in the long run from stealing pots.
When you reach the final table, the blinds will be enormous and you should have by far the largest stack at the table. Shove almost every single hand (exceptions for awful hands and against opponents with stacks that significantly threaten you) and steamroll the competition. You will steal all the blinds as well as most raises before you, and will start to knock the other players out rapidly, so you're basically home free!