How to oust a Tory leader
After becoming Conservative leader in 1997 William Hague oversaw a review of the party's leadership rules. As everyone interested in politics knows the main part of this was to give ordinary party members a vote - Conservative MPs would still get to whittle down the field of candidates to two, but ordinary party members would then pick the final winner (in theory at least, in 2016 that final choice was dodged by Andrea Leadsom standing down).
The other major change introduced by Hague seems to have seeped less well into the consciousness of the Westminster village. You still see the press talking about "stalking horse" candidates sometimes, or talk about such-and-such mounting a challenge against the leader, echoing back to the old rules when people like Thatcher in 1975 and Heseltine in 1990 could directly stand against the incumbent leader. Such a race is no longer possible. Grant Shapps this morning called for Theresa May to call a leadership election. Again, she can't really do that, or at least, not in the way John Major did in 1995 when he called an election and stood himself. The current rules state that if a contest is caused by the resignation of the incumbent leader then that outgoing leader can't stand as a candidate. In short, the only way Theresa May could call a leadership election is by resigning and going away.
Under the current rules a Conservative leader cannot face a leadership "challenge". Instead the way of removing a leader is through a vote of confidence by Conservative MPs, triggered by 15% (currently 48) of Conservative MPs writing to the Chairman of the 1922 Committee saying they would like one. The incumbent leader does not face a challenger or challengers in such a vote, it is a straight Yes or No to whether they should continue in office. If the leader loses the vote, then they cease to be leader and an election for a replacement begins in which the ousted leader is not eligible to stand.
The 48 letters do not need to be organised together, or indeed sent at the same time. They can be a collection of dribs and drabs sent over weeks or months. Right now Grant Shapps appears to be organising (or is, at least, the public face of) those Tory MPs who wish May to go, but there is no requirement in the rules for a "challenger" as such.
Full rules are actually quite hard to find - while the party constitution has some details of the election procedure, the rules for ousting a leader are in a seperate document from the 1922 committee. A full set of the rules is, however, on Tom Quinn's website here.