The March on Rome was very much a P.R. move, and although a fair bit of dirty play was involved institutional procedure was respected.
Prelude
Italy did not come out of the First World War in good shape. Between 1919 and 1920, Italian cities resembled battlegrounds, as frustrated (and often unemployed) demobilized soldiers aligned themselves alternatively with militant communist groups or militant fascist groups, both of which were bent on shaking up the social order. The socialist-dominated governments (Nitti between 1919-1920 and Giolitti in 1920-1921) proved unable to deal with the situation, and by the end of 1920 army regiments in Central Italy were in open revolt.
The Election of 1921
The Italian Elections of 1921 resulted in a three-way tie, with the Socialists winning 24% of the vote, the Catholics (Partito Popolare Italiano, PPI) winning little over 20%, and the fascist dominated "Blocco Nazionale" coalition getting a little less than 20% of the vote.
With prodding by King Victor Emmanuel, moderate socialist Ivanoe Bonomi was able to round up a coalition of moderates thanks in part to a definitive expulsion of filo-communists from the Socialist Party prior to the election. However, the inherent incompatibility of the Socialist agenda with that of the Catholics, as well as Bonomi's leniency towards the fascist militias and repression of non-fascist militants (unpopular with his own party, but necessary to avoid a communist revolution^1 ) meant that this government would resign in February 1922.
The liberal Luigi Facta was then prodded to the premiership by the King. However, the Liberals were minority members in the ruling coalition and the larger Socialist-Catholic deadlock was still unresolved. Facta's cabinet reshuffle on august 1st 1922 did little to make the country more governable.
King Victor Emanuel
The day after Facta's cabinet reshuffle. fascist paramilitaries (who had been growing in power since Bonomi was in office) occupied the city of Ancona. It was a clear provocation^2 , and the government didn't react. In fact, it couldn't: army regiments in Ancona had been the first to revolt back in 1920 and Italian authorities were fearful that the army, who saw the fascist paramilitaries as allies in the struggle against communist revolts, would defect to the fascists if mobilized. This was the first show of force by the Fascists with regards to the government (and not their usual targets, the communists) and it went so smoothly the Fascist leadership began planning larger shows of force from here on.
Four days before the march on Rome, a march on Naples played out without government opposition as a "dress rehearsal" for events that would transpire in Rome. The feeling in government now was that a large-scale confrontation between the government and the fascist militias would be inevitable.^3
On October 27th in cities with large fascist majorities, fascist militias occupied major public buildings while thirty thousand fascist demonstrators boarded trains to Rome. The heads of Italian security forces met with the King and prime minister late that evening. As a testament to the state of utter chaos that the Italian leadership was enveloped in, when the King inquired if the army was inclined to defend Rome, General Diaz answered "The army will certainly do its duty, but it better not be put to the test."^4 The hypothesis of declaring a state of emergency was briefly floated, but the consensus seems to have been that most army units deployed would simply defect to Mussolini, who was the fascist's leader in parliament and at this point in time had stayed behind in Milan (lest the inevitable confrontation be more violent than planned).
The following morning, Facta and his ministers tried to prod Victor Emmanuel into declaring a state of emergency, but the King replied, "The only thing that can follow a state of emergency is civil war. Now, one of us must be sacrificed." It would seem that the king was done with putting together haphazard coalitions to keep extremists out of power, and Facta resigned that evening.^5
Here we can open a whole discussion as to what Victor Emanuel's motivations were, especially because accounts differ with regards to what, precisely, was said. Although the Army's loyalty to the government was dubious, Facta seems to believe they would remain loyal to the King. However, Victor Emanuel seems to have been less certain, especially because there was whispering of a secret pact to usurp the throne between Mussolini and the King's cousin, the Duke of Aosta. The King not only harbored a near-pathological jealousy of his cousin, but the Duke of Aosta was a hero of the first world war (after Cadorna's removal in 1917, Victor Emanuel insisted on promoting Diaz over Aost, who was the preferred choice of the Allied Command) and Aosta was very popular with the army.
The March on Rome
On October 29th a series of telegrams were exchanged between the King in Rome and Mussolini in Milan, culminating in an invitation extended to the Fascist leader to meet the King. On the evening of October 30th, Mussolini arrived in Rome, and met with the King for over an hour. Once an accord was reached in order to form a governing coalition, Mussolini gave word to his supporters to enter the city from all sides. Only one column encountered resistance from left-wing militants. On October 31st, Mussolini's supporters paraded before the king in their iconic black shirts.
The Musolini Cabinet
The first cabinet was composed of, in addition to Benito Mussolini as Prime Minister, three fascists, two Catholics, two social democrats, two liberals (from two different parliamentary factions), one nonfascist nationalist (D'Annunzio's party), the commanders in chief of Army and Navy, and an independent.
On November 16, Mussolini presented his cabinet to the chambers of parliament, and obtained a vote of confidence (306 in favor, 116 against, and 7 abstained). In January 1923, he institutionalized his Blackshirt militias as the "National Security Militia," significantly facilitating the implementation of policy.
Fascist Repression
The following election in April 1924, the fascists obtained 60% of the vote, and constituted a government without resorting to a coalition. However, the results were contested as fraudulent, especially by the leader of the Socialist Party Giacomo Matteotti, who brought the matter before parliament (Matteotti would later be found murdered on June 10th, 1924).
The following election in 1929 the ballots listed only fascist candidates and the options were "Yes" and "No." "Yes" gained 98% of votes. The next elections were held with the same system in 1935, and 99% of citizens voted "Yes." These two times, there was no opposition to contest the results, however the consensus is that they were fraudulent.
Source: Le origini della guerra civile: L’Italia dalla guerra al Fascismo Fabio Fabbri, (UTET) Turin, 2009.
As for English Sources I'm not sure how how outdated you consider Italy from liberalism to fascism, 1870-1925 by Christopher Seton-Watson, but I'd assume it gives a good overview (my textbooks cite it as an english source). I'm very sorry I don't know of anything newer in English, I'm not active in academia and believe it or not this sub is my primary source of updates on english-language scholarship (please don't de-flair me!). The main problem when discussing post-unification Italian history (and why I avoid it) is that interpretations are still very politicized to this day, and good source material is hard to come by.
Footnotes:
It is unclear how much of this policy was requested by King Victor Emanuel. Certainly, the King was fearful of ending up like the Tzars of Russia and was also fearful of using the army, possibly suspecting that the armed forces wanted to depose him in favor of his more popular cousin, the Duke of Aosta.
The Fascists had been looking for a chance to demonstrate their strength "on the ground," and the signal was clear: while the government in Rome is weak (and excludes us), the Blackshirt Militia take what they want.
There even was an attempt to organize a counter-march of moderates, but moderate people unfortunately don't tend to form armed militias.
Translation: LOL no.
King Victor Emmanuel seemed to believe he could use the Fascist's militia to stop both the communists and the army from deposing him, while limiting Mussolini within a coalition of the right in Parliament. The scheme obviously didn't go as planned.