Well first you had to pass, and pass brilliantly. After that, your day-to-day life would have been very different based upon your posting. I'm not familiar with the Song, but I am much more well-acquainted with the Ming/early Qing. As a low-level civil servant, serving at some magisterial level, you would almost certainly have been bombarded with an endless stream of miscellaneous tasks, ranging from sorting out murders to mediating disputes over filial piety. China has long been blessed and cursed by the Imperial exam system as it created a heavily centralized and culturally homogeneous bureaucracy in a very, very diverse country, but simultaneously ingrained a culture of rule-by-men as opposed to rule by law, and nowhere could this be seen better than down at the lowest levels of the Imperial bureaucracy. There were obviously also other positions you could be placed. The three highest scoring candidates for the Imperial examination (the exam system as a whole is better referred to as the Civil service exams as the Imperial exam was actually a specific level of it) often would receive appointments to the Hanlin Academy to provide discourse on the interpretation of Neo-Confucian and Confucian canons. If you did commendably, you might also be appointed as a tutor, or to the ministry of Rites to aid the court in conducting Rites in accordance with the ideals of Confucianism. In terms of power, it varied directly. Zhang Juzheng was the regent for the Wanli Emperor in the late 16th century when the emperor was yet to come of age, and in that time he wielded considerable power. Granted he wasn't particularly terrible administrator, but he was still able to flex his political muscle and bend the rules of the court to his will, and managed to guide the young emperor into accepting his policies, at least while he lived.

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I really can't think of any modern comparison in the civil sector... officials could do basically whatever they felt necessary to adhere to the edicts of the emperor and so the closest I could think of would be military officers. Anyways, if you want to get a feel of what life was like for the upper-class, scholar-gentry, you should definitely read The Peach Blossom Fan, Dream of the Red Chamber, or some of Feng Menglong's works. Vernacular pieces provide a very, very good look into the actual lives of these kinds of people during the mid-late Ming and early Qing. You can also read source documents... if you know literary Chinese, or secondary source documents like Confucian Image Politics, which I personally recommend.

This is certainly one of the most complex questions that could be asked, considering the multitude of functions provided by the Chinese Imperial Government in all walks of life. Having taken a handful of ancient Chinese history courses in Peking University, I would like to give a simple walkthrough by giving a few notable examples.

The arguably most important and coveted position would be that of the Imperial Chancellor. The question of what constitutes the imperial chancellor(宰相 zai xiang) is a frustratingly complex issue, as during Song history, not only were there numerous Chancellors at the same time, but the actual job that is considered to be chancellor changes from time to time due to reforms (It was 同中书门下平章事 at first, but it experienced a variety of different names and actual roles of being 尚书左右丞/左右丞相 etc.). Interestingly, never had the Song ever created an actual position called "Zai Xiang", much like how there is no position actually called "head of state", instead would be "president","king" etc.

The actual responsibilities of the Song Chancellor also changed from time to time, such as there being a divide between the chancellor and the head of the Song Treasury(三司使) at the beginning of the Northern Song, but merged roles after Emperor Shenzong thought it was stupid that the government was given such a major separation of power (though the Song encouraged power separations in earnest). In times of great peril, chancellors were also known to become military commanders (some of them being surprisingly competent, given their mostly academic upbringing), though they usually did not have that power. But overall, I would say while there is nothing similar to a modern UK MP, the Song Chancellory does function similarly to the UK Cabinet, though with an absolute monarch making the official decisions. There is almost no range limit on what decisions the Chancellors can discuss and decide on, from diplomatic decisions, establishing new strategies in warfare, to enacting major reforms, and just dealing with the reports sent from everybody down below, Chancellors have the power directly give commands (this power is often under a tug of war between the emperor and the chancellor), but mainly they discuss amongst themselves and with the emperor in cabinet meetings and the emperor calls upon his scribes to write it down to eventual release these documents as decrees of the empire, thus making everything official (of course, low-level orders exist outside of the emperor's oversight, since he can't do EVERYTHING). I disagree with the view that the Chinese are a completely "rule-by-man" system, ancient China has a very extensive written law system, along with extensive traditions, much like the UK. Though it certainly isn't rule of law. The Chancellory can repeatedly block the emperor's attempts at naming his favorites as bureaucrats due to the system design of 门下 department having a rebuking power, and the Song emperors have a major commitment to their family creed, such as not killing any bureaucrats on a whim. I would say the Song definitely have a somewhat professional government, though the ambiguities, and the fact that it isn't rule of law makes it very different from true modern governments.

Roles in the 御史台 (yu shi tai) is interesting as well. While this department had seen many mergers and changes, its roles remain unchanged, being one to check down on corruption and to tell the Emperor the hard truth facing his country no matter the costs. Some of its members would patrol the country to look for official misconduct. And others are stationed in the central court to warn the emperor of any mistake they feel the emperor is making, such as thinking his trust in a certain person is misplaced, etc (By norm, the emperor can't kill them no matter how angry he gets).

There are also librarians, who for the most time stay in the imperial library, correcting spelling mistakes and answering calls for the emperor when he needs scholarly advice. The Han Lin Xue She (翰林学士), being the scribes are mentioned earlier, serve as critical advisors and actual writers of the imperial decrees.

Of course, you also get prefectural and county level governors, and semi-province governors above them. These people do the real maintenance of the empire, going from deciding on local policies, stopping famines and riots, promoting education, building infrastructure, dealing out legal decisions (though death penalties require clearance from the Emperor himself as per law, or you get killed for overstepping your place) and all sorts of stuff. There also officials for the imperial departments and their local branches, some of them were responsible for giving out social welfare in the form of seed loans to farmers, and others that manage the economy by purchasing certain goods when prices became too low, and vice versa. There are enormous amount of clerks on payroll who filter your everyday documents and police the streets at every level of the Song government.

The arguably most exciting thing you could dream of as a Song bureaucrat would be being called upon to lead the empire's forces in to battle against all sorts of peasant revolts and nomadic invaders. High-ranking officials were sometimes given the authority of 安抚使 or 宣抚使, essentially "the peace-making envoy", to take command of Song troops and route enemies. There are professional generals of course, but the Song emperors have a tradition that distrusts the military and they usually want somebody more loyal when we're talking about troops numbering in the tens of thousands, though the generals tend to be responsible for the actual-on the-ground action.

I would argue that if not considering the modern system and ideology changes, the actual things done by Song bureaucrats would be very similar to the modern day. Handling documents, collecting taxes, surveying fields, supervising on work and so forth. And they were a relatively rich and respected lot in their society, and some government roles were almost designed to give you an easy life and no power at all.

I wrote this answer to be a bit more example-based so that you can get the detailed picture (I hope), and I also hope this answers your question.