I accepted an at-will contract offer with Company X, and before the employment start date I interviewed with and received a job offer from Company Y. I prefer the offer from Company Y and I intend to sign the contract tomorrow, before the start date at Company X. How can I politely inform Company X I am reneging on their contract without burning bridges? How much information, if any, about my new position at Company Y should I disclose?
You can politely inform company X.
You shouldn't mention anything about Y or why you're quitting. Just "due to changes in my personal circumstances I'm unable to take up your offer anymore".
Nothing else you say is going to make them feel any better, and will potentially just make them more annoyed than they're already going to be, so just don't say anything.
That covers the being polite part.
You can't do it without burning bridges.
Unless you have a really good excuse (like, say, one of your parents just died and you have to move cross country to take care of the other one) they're going to see this as what it is: You accepted a contract, and then reneged.
There's not much to be done about that unless you decide to stay anyway.
I wouldn't feel bad about it. They may not like it, but they did make it an At-Will contract. If they don't want this to happen then that's on them to change.
How can I politely inform Company X I am reneging on their contract without burning bridges?
You have to accept that the bridge will be burned. There is no alternative. You can't call them a week or a month later and say, oops I want to join.
The polite thing you have to do, is do it as soon as you accept the other position. That gives them time to switch gears. It gives them time to contact the next acceptable person on their list.
How much information, if any, about my new position at Company Y should I disclose?
Unless there is a signed contract that says the only way out is if X occurs, there is no reason to get specific. Just tell them that you have decided to go in a different direction. There is no need to negotiate with them so they don't need any information to use to make a counter offer. Some will ask about the reason so they can learn, but you have no obligation.
If you have received anything from them or they have already shipped an item to you, you must return those items. If they gave you a signing bonus, or have given you money to move, check your contract regarding timelines for returning those funds.
I accepted an at-will contract offer
In some places including the United States almost all jobs are at-will. That doesn't make it easier to tell somebody you quit, and it doesn't prevent them from getting upset.
It seems entirely appropriate to me.
An at-will contract means they consider you to be an easily replaced pawn. You don't owe them anything but fair treatment.
You are not reneging, you are excercising the exit clause of the contract.
Politely inform them that you no-longer wish to be an employee.
Tell them as much about your new position as you wish to, they are not entitled to any information.
Give them reasonable notice. Do not share details of the offer you are considering, but consider a counter offer if they give one. Don't try to create enter a bidding war, especially if their counter offer is another at-will contract.
They will remeber you as someone who knows their rights, if that is cause for them not to hire you at some future time you probably do not want to work there.