They're running multiple cases at once.
In the instance of Heller, they took the plaintiff's arguments last month, respondent's arguments this month, will hold 30 minutes of oral arguments next month, and likely issue a verdict around June.
They're processing a lot of other cases during that time period.
About 40 briefs will be submitted total, up to 9,000 words each. While that's a bunch of heavy reading, it's not that bad if your job entails reading a lot of heavy briefs.
Each judge has a staff of clerks who do a lot of the gruntwork related to each case. I imagine (others may know better) they'll assign one clerk to each brief to read it, pull up related material, write insightful summaries, check for accuracy, etc. (example: DC used a particular quote to justify something, Heller noted that DC left off part of the quote which completely changes the meaning of it, and now some clerk has to go dig out the source material and find out what's going on, and then write a concise memo to Justice Thomas saying "DC lied, here's why").
Ultimately, the Supreme Court does things however they want.
