Generally, if you were married for less than two years at the time of your marriage-based green card interview, what you would receive is Conditional Permanent Residence - permanent residence that has all the benefits of regular permanent residence but lasts only two years. Normally, nothing will automatically happen to invalidate this Conditional Permanent Residence status simply on account of the divorce becoming final.
In the three-month window before the two-year Conditional Permanent Residence period ends, you are (in normal, non-divorce circumstances) supposed to apply jointly with your U.S. citizen spouse to remove the conditions and get a regular green card (unconditional permanent residence).
If the marriage is no longer viable, there are a few ways this petition to remove conditions can still be done successfully, assuming that the marriage was a legitimate marriage that simply didn't work out. It depends on the timing of the divorce (whether it is final), whether your ex- or soon-to-be-ex spouse is on good terms with you, whether you can otherwise document the bona fide nature of the marriage, and whether there was a provable abusive situation within the marriage.
You really need to speak with a lawyer about the nature of your current status and the future of this status.
It is no longer a given that you lose your opportunity to keep lawful permanent resident status if you get divorced within the conditional permanent resident period which is the first two years. The law has changed to favor the immigrant's right to stay even if the marriage failed within just two years.
However, this is only if the immigrant can prove that the marriage was bona fide, meaning legitimate, love, good faith, and not just to obtain a green card for an immigration benefit. The form that is filed to lift the conditions from the conditional permanent residency is the I-751.
It can get a bit complicated on the timing of the divorce decree. There's the 90 day window for filing the I-751, and if the ex wants to help or not on the joint petition-- of if you are filing for a waiver -- on the form, as well as filing on your own. There are also other grounds such as abuse. Gather documentation if that is the case.
It would be a smart idea to seek the advice of an experienced immigration attorney, whether at a legal clinic or private practice. Charities like the Catholic Charities and United Way, First Call for Help may be a starting point for you.
One writer mentioned that you have a permanent lawful residence or green card-- you don't yet! The writer mentioned no way to lose it other than crimes. This is not completely true! There are other ways to lose the status. One of several would be abandonment. If you went back to Canada to reside, you would likely abandon the status -- and if an I-751 is never filed, the CPR status won't just convert to LPR status.
Being married for one year means that you got your green card based on the marriage and that you are a conditional green card holder. The same form ( I -751) can be used to file for removal of the condition or for a waiver. A waiver means that you are filing for the permanent green card on your own (without the spouse) in the 90 day window before its expiration based on a bona fide or good faith marriage.
This requires a showing that the marriage has been a viable one, so you would need to show financial commingling of funds, etc.. You would also need to get a divorce, but the date of separation is critical on the divorce complaint. There are also other options to file if there was any mental or physical abuse, but the filing is very fact specific. You would really need a good attorney, or you could risk the loss of your green card.
I agree with the comments made by the attorneys above (Mr. Reich, Ms. Schneider, and Ms. Beach). However, I would emphasize that it is important to speak with an experienced immigration attorney about your situation. For example, during the year since Mr. Reich first answered this question, the immigration agency has issued new guidance memoranda about the I-751 "Removal of Conditions" waiver.
Failure to follow the immigration agency's new guidance may have a negative impact on your petition. It is imperative that you contact an experienced immigration attorney to ensure that your waiver petition complies with current immigration agency policy.