The particular question you ask makes the question more difficult than most.
To eliminate the electoral college would require a constitutional amendment.
There are two ways to start the amending process. To the best of my knowledge, only one of them has ever been used.
The first way is for a proposed amendment to pass both houses of congress by a 2/3s vote (2/3s vote of a quorum in attendance, not 2/3s of all
members)
The second way, which has never been used, is for 2/3s of the State legislatures to pass resolutions calling for an amending convention.
en.wikipedia.org...
When the first way is used, the proposed amendment goes straight to ratification, because it's already been specifically proposed.
If the second way were to be used, there actually isn't an amendment proposed yet, only a convention to form amendments. The federal government is
then required by the constitution to arrange a meeting of state deligates who will draft any amendements they wish to make. If the convention agrees
on amendments, then those amendments can go to ratification.
Ratification can work in one of two ways. The method is chosen specifically- it's one or the other, not a combination.
The most common way is to have the State legislatures vote on ratification. 3/4s of the states (rounded up, as always) must accept the amendment for
it to pass.
The second option was only used once (not counting the adoption of the constitution itself). It was used to repeal prohibition with the 21st
Amendment. This was done because even though everybody wanted to do it, there were a lot of politicians who didn't want to be blamed by the
temperance proponents for being the ones who repealed it- it would look bad on them. So they washed their hands of it and let the people decide for
themselves.
When that happens, the states hold a referendum election where the citizens can vote the amendment up or down. 3/4 of the states are required. The
states can make their own rules on how they vote to ratify- they can require a simple majority, or they can require 2/3s, or anything else that state
law provides for. (the same way that the current electoral system works- the states get to choose how the voting in their state works)
Now, for the private citizens of the US to actually MAKE it happen, there's really only one way, other than just threatening not to vote for people
if they don't do it.
24 of the 50 states have a referendum process for passing laws. The way that works is that you have to gather a certain number of signitures in
support of a bill, and if you get the required sigs, it goes on the ballot for a yes/no vote in the next election (usually even-year elections),
except in the case of Arnold's Special Election and other such cases.
You can't actually propose an amendment to the US Constitution that way. But you can pass a law that requires your state legislature to demand an
amending convention. The problem is, you need 2/3s of the states, which means you need 34 states. Only 24 states have the referendum. So you need to
carry referendums in all 24 refendum states, then hope that 10 more states will feel the pressure and realize that the people want it, causing them to
vote for a convention without a demand by referendum.
Even then, you haven't passed an amendment, only gotten a convention. It's still up to the delegates to write the amendment you wanted, and then
you've got to get it approved by 3/4 of the states (38 presently).
It's very very difficult. Almost impossible. The last amendment to be adopted was in 1992, and believe it or not, it was passed as a practical joke.
In 1789, an 11th amendment was proposed that would stop congress from giving itself pay raises in the same term. It was proposed successfully, but was
not successfully ratified.
In 1982, 193 years later, a college student in Texas realized that the amendment did not have a sunset clause, and so could still be ratified if the
states took action. So he started a campaign to pressure states to ratify it. In 1992, it was finally ratified.
Not counting that, the last time the constitution was fully amended (as in, the last time that an amendment was successfully propsed and ratified, not
just taken off a shelf after 200 years in the dust) was in 1971. It's been 34 years.
It does stand mentioning that there is an amendment still technically pending ratification from 1789 that, depending on supreme court interpretation,
would probably either cut the house in half or expand it to almost 6,000 members. If it was interpereted the first way, it would become much harder
for democrats to win in the electoral system. If interpereted in the second, an election such as the 2000 election would in the future go Democratic.
The random factor and the election-rigging motive make it completely unpassable fo course.