We don't know. What we do know is that it varied, because Montfort's 1265 parliament was aimed at rallying the support of clergy and communes, the latter of which were the ones sending these urban representatives, and they had their own systems. But the one thing we can say for sure about the parliament of 1265 is that it was not preceded by a General Election - there wasn't time.

The first thing to note is that the ideological groundwork for Montfort's parliament was not his. In the short term he inherited the ideas of his predecessor Hugh Bigod. Longer term, the idea of a representative government had been kicking about in England since at least 1215, when King John was supposed to give up his powers to a council of barons. Although this did not come to fruition due to the resumption of the war between John and his barons, and then the death of John, the idea remained. Magna Carta wasn't actually trying to bring about what we would call a representative government, but people seem to have gotten excited and interpreted it as that. As one chronicler noted disapprovingly of 1215:

"England has ratified a perverse order. Who has heard such an astonishing event to be asserted... for the body aspired to be on top of the head; the people sought to rule the king!"

This went hand in hand with a rapid growth in the medieval commune movement, in which towns and cities negotiated, bribed, and occasionally rioted their way to securing devolved local governments free from the interference of the nobility. Each commune decided their own rules, but many incorporated elements of representative democracy with cities often being divided into wards that chose a local official (usually called an Alderman) to run the ward and represent the ward at the city council. Other towns and cities organised themselves strictly according to guilds - each guild would elect a representative to sit on a town council made up of guilds. How aldermen were elected in this period is unclear, but there does seem to have been an element of choice on the part of local residents. Even if aldermen and other officials were appointed rather than elected, the clamour of the mob could see that any particular person was or was not chosen. The early 13th century was early days for these quasi-democratic communes in England - London only seems to have switched to annual mayoral elections in 1212 - but the idea of representational government and elections were around and many people, particularly urbanites, wanted a less aristocratic society and expected to be able to participate in their local politics even if this wasn't in the form of lining up to cast votes. The most detailed picture of local government we get is 14th century London (we have their constitution from 1376-1387), which sets out an electoral college system for mayoral elections. Whether that was common or exceptional, we don't know.

When the barons took control of England in 1258 they had no manifesto, they only agreed that Henry III was too incompetent and out of touch to continue. To quote from page 37 of Baronial Reform and Revolution in England 1258-1267:

"The reformers' failure to lay out their programme did not go unremarked at the time. When narrating how the Londoners (in July 1258) were asked to accept the 'statutes of the barons', Matthew Paris remarked that the barons 'still did not plan to publish what had been established'. One surely detects here a note of puzzlement, even of frustration. Later, Paris seems to have died in the middle of copying a draft of the legislation that became the Provisions of Westminster, perhaps from the sheer excitement of at last having something to copy."

So we fast forward to 1265. By this point two important things have happened. Firstly, Henry III has escaped captivity and raised an army with a plan to take down the baronial government and restore the power of the monarchy. Secondly, the initial leader of the government, Hugh Bigod, died of natural causes and Simon de Montfort emerged as the new leader. In May 1264 it was clear that although the baronial government was more popular than the monarchy, that popularity did not translate into soldiers. Although Henry III and the barons were not constantly fighting - Henry even attended Montfort's parliaments - it was clear that if Henry did decide to just kill Montfort, he could probably get away with it. To guard against this possibility, Montfort first tried to capitalise on his support among the English clergy by proposing a peace summit led by them. Despite generally opposing the revolution in 1258, they had come around to the programme of reform. Simon de Montfort hoped that Henry III's piety might sway him into accepting ecclesiastical authority and give Montfort a diplomatic advantage. The monarchists saw through this. Given that thoughts and prayers from the clergy weren't going to help on the battlefield, Montfort needed a way to raise money and men in the knowledge that much of the nobility were either hedging their bets and not offering troops to anyone, or going over to Henry III. In particular, the barons needed the support of the Earl of Gloucester, but his committent to the cause was wavering.

Montfort held his first parliament in mid-1264, in which he asked each county to provide two knights chosen by the county court. In practise, this meant it was left to the sheriffs. Although county courts could theoretically organise elections from a list of candidates (and did so later in the Middle Ages), it is unlikely that this ad hoc parliament had the organisational ability to pull that off. The 1264 parliament was a disappointment to the barons, because although it passed sweeping reforms it did not provide a long term alternative system of government, which is what the barons needed to keep Henry sidelined. Six months later it was time for the next parliament and something had to change to revive baronial authority.

This is where the boom in the commune movement comes into it. Senior figures in the baronial government had been struck by how Londoners had forced their government from a position of neutrality to support of the barons in 1263. Many other towns and cities were fervent supporters of the barons, and had been impressed by Bigod's programme of systemic administrative reform that Montfort had continued. When the barons travelled to towns and villages to listen to their complaints about how the royal administration had failed them, they were often pleased by the willingness of local people to call out failures of government and engage with the new system the barons were trying to create (whatever that was). Documents issued by the new government increasingly referred to England in terms that urban communes would have recognised; stuff like 'commonwealth' and 'res publica'. By the mid-1260s, the barons modelled their image on the devolved communes that had swept England in the preceding decades, and at some point Montfort realised that the communes were an untapped source of support that could be taken advantage of at parliament. So he talked to Henry III and got him to agree to summoning men from the communes in the hope of providing stability for England.

Notably, we don't know how many representatives actually showed up, nor were there any instructions for how representatives should be chosen. The summons from Henry III simply said:

After the grave perils of the recent disturbances in our realm, my dearest firstborn son, Edward, was delivered as a hostage for securing and confirming the peace in our realm, but now, blessed be God, the disturbance has been settled. In order to provide happily for his release, and also to confirm and finally complete the tranquillity and peace of the realm it is necessary that we should have discussion with our bishops and barons, and to that end we require your advice. I ask, in the faith and love in which you are bound to me, and setting aside every other matter or reason, that you should be with us at London on 20 January 1265, to discuss these things, with us and with our bishops and barons, whom we have caused to be summoned there.

This could not be vaguer if it tried. The accounts of the parliament itself don't help. For example:

This year, on the Octaves of Saint Hilary, by summons of the king, all the bishops, abbots, priors, earls and barons of the whole realm, and also the barons of the Cinque Ports [representatives from the ports of Kent], and four men of every city and borough came to London to hold a parliament. In this parliament, on Saint Valentine’s Day, it was made known in the chapter-house at Westminster, that the king had bound himself by his charter, on oath, that neither he nor his son, Prince Edward, would from thenceforth aggrieve, or cause to be aggrieved, the earls of Leicester or Gloucester, or the citizens of London, or any of those who had made alliance with them, on the pretence of anything done during the time of the past commotions in the realm. And the king expressly gave orders that the Charter of Liberties [Magna Carta] and the Charter of the Forest, which had been made in the ninth year of his reign [1225], together with the new articles which had been enacted in the month of June in the forty-eighth year of his reign [the 1264 parliament], should be inviolably observed.

The only thing we learn for sure about the process of choosing urban representatives from contemporary documents is that there was only one month between the summoning of the parliament and its beginning, which makes it unlikely that there were direct elections for any of the local MPs. There simply would not have been time to arrange anything genuinely democratic even if they wanted to. Instead, given the extremely short notice, it is far more likely that local town councils chose someone themselves according to whatever systems they already had for choosing officials and representatives.