The 25th Amendment cannot be executed by a single party. Instead, it takes a few steps of approval by multiple parties.
The vice president is the primary starting point for invoking the 25th Amendment, specifically the fourth section. The vice president, in conjunction with either a majority of the executive Cabinet or a specific "body" designated by Congress, must invoke the Amendment in tandem.
The vice president takes over once these parties submit a formal written declaration to Congress. If the president refutes this, they can return to power for four days, in which time the other parties can again submit a declaration invoking the president's removal. If this happens, the VP takes over again and Congress must secure a two-thirds vote in both the House and Senate within 21 days to permanently remove the president.