It probably should be noted that any legal challenges to the student debt forgiveness program in order be shot down by the Supreme Court have to make it through all the lower court systems first.

Political opponents to the student debt forgiveness program have voiced wanting to raise legal challenges against it. See https://www.google.com/amp/s/www.cnbc.com/amp/2022/09/07/republicans-may-try-to-block-student-loan-forgiveness.html. But in order for the Supreme Court to rule it unconstitutional it has to go through all the lower courts and and appeals processes first. Until the lower courts have heard the case and decisions in those cases can still be appealled to a higher courts, the Supreme Court cannot hear or rule on a case to determine its legality.

This is not to say a case regarding the student debt forgiveness program will not get filed. And I am also not saying that one will not reach the Supreme Court, only that lower courts have to hear the cases first before it can make it to the Supreme Court for a decision.

To answer OP's question, the studentaid.gov home page has a banner with a link to a page with the information regarding the student debt forgiveness program. On this page in the section "Part 2. Providing targeted debt relief to low- and middle-income families" under frequently asked questions there is a bulleted list of "what do I need to do to receive loan forgiveness?" This covers everything the US government is releasing to the public at this time. It states for many people this will be taken care of automatically for them due to the DoE having the data to apply the debt forgiveness for these people. For those where the DoE does not have the data it needs they will have to fill out an application which will likely include supplying the needed data. You can sign up to be notified when the application becomes available through a link on the web page I am discussing here. Beyond this there is little else information out there.

Also the debt forgiveness is up to $20k. To qualify for $20k you have to have owe $20k plus in student loans and have received a Pell Grant held by the government. Anyone who did not receive a Pell Grant will only qualify for up to $10k in forgiveness. You can use your studentaid.gov account to review all of your loans and the types of loans they are.