There are two ways. The first -- often described as the "nuclear option" -- is relatively straightforward.
The Senate's presiding officer -- played by a friendly vice president -- would make a ruling saying the Constitution allows the Senate to change its rules by majority vote. That would allow a simple majority to rewrite the Senate's filibuster rules.
That ruling could be appealed by Republicans -- who could then filibuster their own appeal to delay, or end, debate.
"The goal is to derail the majority's effort to change the rules by majority vote," said Brookings Institution Senior Fellow Sarah Binder.
But, "according to precedent," Binder said, Democrats could simply table that appeal of the presiding officer's ruling, and go directly to an up-or-down vote.
From there, secure 51 votes and you can reform the Senate's filibuster rules anyway you want.
And, according to Binder, that doesn't have to be done at the outset of a new Congress. That's just a matter of tradition. If the Dems really wanted to, they could go through this process anytime they wanted.
The problem is political.
"It's a brute force move that basically blatantly ignores the existing rules," said Norm Ornstein, resident scholar at the American Enterprise Institute. "It would be the equivalent of in a Super Bowl game, a team basically tackles all the referees, ties 'em up and throws them onto the sidelines and declares that a penalty is invalid."
Reforms by ruling have occurred in the Senate in the past -- but mostly for much smaller things, Binder said, like jump-starting debate on a nominee. To use the "nuclear option" on something much bigger -- like filibuster reform -- Binder believes the majority would have to be absolutely "convinced that what they're doing is going to be popular."
Not to mention the fact that Democrats almost certainly won't have a Senate majority forever. So whatever watering down of the filibuster they push now might end up hobbling them when they become the minority again one day.
"As long as senators think like that, they're gonna think twice about giving up their own parliamentary rights," Binder said.
Ornstein notes that the "nuclear option" wouldn't be quite so nuclear if it came at the beginning of a new Congress. In that case, the presiding officer's ruling would be a little different -- essentially, that the Senate isn't a continuing body, and has the right to rewrite its rules when new members join, rather than that the Constitution gives the Senate the right to write its own rules carte blanche.
There's another way, too -- but Democrats almost certainly don't have the votes.
Sens. Tom Harkin (D-IA) and Jeanne Shaheen (D-NH) have cosponsored a proposal that would essentially lower the eventual vote total needed to overcome a filibuster from 60 to 51.
On the first cloture vote, 60 votes would be needed to end debate. If one did not get 60 votes, one could file another cloture motion and 2 days later have another vote. That vote would require 57 votes to end debate. If cloture was not obtained, one could file another cloture motion and wait 2 more days. In that vote, one would need 54 votes to end debate. If one did not get that, one could file one more cloture motion, wait 2 more days, and 51 votes would be needed to move to the merits of the bill.
So what would it take to pass a bill like that?
Getting that bill to the floor wouldn't just require the normal (and apparently unattainable) 60 votes. Because it would rewrite the Senate's rules, it would take a two-thirds vote (probably 67 senators) to break a filibuster and get Harkin's and Shaheen's proposal to the floor.
It would then require another two-thirds vote to break a filibuster and force an up-or-down vote on such a proposal.
That's happened before, Binder notes -- in 1979, when a 100-hour limit was placed on post-cloture filibusters; and again in 1986, when that time limit was reduced to 30 hours. "It's not impossible," she says -- it's just not common.
But with Democrats unable to secure even 60 votes to push ahead on its legislative goals, it seems highly unlikely -- if not outright impossible -- that they'd be able to round up eight Republicans willing to water down the minority's filibuster power.
But the reform-by-ruling nuclear option? That's very doable -- at least technically speaking. Politically? That's another story.