In March 2020, the Court postponed oral arguments due to the pandemic, noting that doing so was “not unprecedented. The Court postponed scheduled arguments for October 1918 in response to the Spanish flu epidemic. The Court also shortened its argument calendars in August 1793 and August 1798 in response to yellow fever outbreaks.” Two months later, we had unprecedented arguments — via telephone, following a different model, and available to the public to listen in live.
The Court has not yet said what it will do for the October 2021 term. There was considerable speculation that it would return to in-person arguments, but that was before we saw the full impact of the Delta variant. I’ll update this page when I can, or check the Court’s page on covid announcements. On the substance of argument options, Scotusblog has an interesting symposium; I fully agree with Lyle Dennison’s critique of the way arguments had been conducted by phone, although others at that symposium feel differently.
To listen in live (if that’s still happening in October)
C-SPAN appears to be the most reliable stream. Also, Scotusblog.org occasionally hosts the C-SPAN feed along with its own live-blog of some cases (for others, they just link to c-span).
Arguments begin at 10am Eastern, with each case typically scheduled for one hour but running long now that the arguments are online. C-SPAN offers different links for each case being argued that day. Last spring, it was necessary to follow a different link for the first and second arguments, although now it seems that you have the option to just keep the first argument’s link open if you want to listen to both. Either way, the second argument often does not start until significantly later than 11:00. (There are always preliminary matters at 10, so the second argument always starts a bit after 11. But during telephone arguments, the Chief was allowing parties and Justices to take much more time than usual.)
Apart from live streaming, there are various ways to take in the arguments after they are completed.
In addition, on Oyez you can get transcript-synchronized audio (the transcript scrolls and highlights automatically as you listen). It’s a great service. Click the case name then click the link in the left column. It takes a little while for these to be available after the audio release, but they seem to be fairly quick.