With an the recent talks that Pelosi is going to "discuss" the 25th amendment in order to get rid of president Trump, what is the process for this? Does it have to be voted in Congress and then voted in the Senate?
The process is outlined in the amendment itself. It requires agreement by the vice president and "a majority of either the principal officers of the executive departments or of such other body as Congress may by law provide." Congress has no say in invoking the amendment. (The senate is part of congress, by the way.)
The Twenty-fifth Amendment (Amendment XXV) to the United States Constitution says that if the President becomes unable to do his job, the Vice President becomes the President
No, it does not say that. It says that if the president is removed from office, dies, or resigns then the vice president becomes president. If the president is merely unable to "do his job" then the vice president may become acting president by one of two mechanisms. The first is through the president's own declaration, and the second is the mechanism under discussion here.
Also, as the speaker is the second in presidential succession, doesn't she have a clear conflict of interests, especially with the well known hatred between the president and the speaker?
Sure, but all she can do is convene a body to discuss invoking the 25th amendment. She can't actually invoke it.
Congress does have a role in resolving a dispute between the president, on the one hand, and the vice president and a majority of the cabinet, on the other, about whether the president is in fact able to "discharge the powers and duties of his office." But if the president thinks he is able (and is able to say so), and either the vice president or at least half of the cabinet thinks he is able, then congress has no say in the matter short of impeachment.
The relevant part of the amendment:
Whenever the Vice President and a majority of either the principal officers of the executive departments or of such other body as Congress may by law provide, transmit to the President pro tempore of the Senate and the Speaker of the House of Representatives their written declaration that the President is unable to discharge the powers and duties of his office, the Vice President shall immediately assume the powers and duties of the office as Acting President.
Thereafter, when the President transmits to the President pro tempore of the Senate and the Speaker of the House of Representatives his written declaration that no inability exists, he shall resume the powers and duties of his office unless the Vice President and a majority of either the principal officers of the executive department or of such other body as Congress may by law provide, transmit within four days to the President pro tempore of the Senate and the Speaker of the House of Representatives their written declaration that the President is unable to discharge the powers and duties of his office. Thereupon Congress shall decide the issue, assembling within forty-eight hours for that purpose if not in session. If the Congress, within twenty-one days after receipt of the latter written declaration, or, if Congress is not in session, within twenty-one days after Congress is required to assemble, determines by two-thirds vote of both Houses that the President is unable to discharge the powers and duties of his office, the Vice President shall continue to discharge the same as Acting President; otherwise, the President shall resume the powers and duties of his office.
Addendum
I will add that when I wrote the above, I overlooked one possibility, which is apparently what the speaker has in mind: Congress can, under the amendment, remove the cabinet from the process by designating a "body" to take its place. The law could also allow the vice president to act in consort with either the cabinet or the designated body.
The power to designate this body is reflected in the amendment with the phrase "such other body as congress may by law provide." But this does not remove the vice president from the equation, because the amendment clearly requires both the vice president and "a majority of either the principal officers of the executive departments or of such other body as Congress may by law provide."
A plan to create such a body also brings the president into the equation, because the president's assent is required to enact a law unless congress can override the president's veto, which is not likely given the current composition of the senate.
As I looked at the text of the amendment more closely, I noticed that there is a difference between the phrase describing who may declare the president unfit and the phrase describing who may challenge the president's declaration that he or she is not unfit. Specifically, the first phrase uses "principal officers of the executive departments," while the second uses "principal officers of the executive department." I suppose the use of the singular in the second case is an error, and that the difference therefore does not affect the interpretation of the amendment, but I have asked a question at Law to see what they have to say: Is the typo in the 25th amendment significant?
s/get rid of/sequester/
. The purpose of the XXV isn't to "get rid of" an officeholder, it's to make sure the office is in fact held, if it should happen that the current officeholder isn't healthy enough to continue. That is, if an officeholder is so unwell that they'll be unable to perform any of their duties for the foreseeable future, their illness has in effect already removed them from service, and in the power vacuum others will probably fill in the duties of said office without sufficient recognition or accountability.