The same as always? Pay old debt with new debt. Other countries might run into issues with exchange rates this way, but the status of the USD is dampening such effects.
Even assuming there are always people, institutions and countries eager to buy the new debt, the government must still pay the ongoing interest on the debt. The concern is when that interest becomes a significant part of the annual budget. Then there is no money left to pay for the essentials - like, /s - government workers' salaries and retirement and military.
You can pay the ongoing interest with more debt. Sure, this will probably not work forever, not even for the USA and the special status its currency has. But "forever" is usually not a relevant concept for politicians.