Originally Posted by Ruhr

Besides checking UA's SDC rules in the Wiki, one bit of practical advice is to get the United app on your mobile phone. Once you check in at T-24, check the app and the "switch to another flight" option appears if there is something available in your fare class. Since you want to delay your flight to the next day, see if there's a confirmed seat for a flight that you are willing to take. If so, then switch to it. Don't delay too long. Sometimes those flights disappear from your options.

Check your app often!