This is one of those "really interesting; difficult to answer" questions, because servants left so little evidence of their personal feelings and life histories. The are diaries written by Thomas Kilgallon, valet to Sir Henry Gore-Booth in the late nineteenth century, but they've never been published or even digitized, as far as I can tell, and are only available to read in hard copy in the Belfast Public Record Office. So, if you're in the area ... There's also What the Butler Winked At, a memoir written about service during the same period.

The general view of domestic service in the period was that it was a feminine thing: most servants were women, since middle-class households that only employed a few were resting on the backs of general maids and female cooks and perhaps a nursemaid, and most of the time it was seen as the wife's duty to manage the servants. As a result, male indoor servants often felt tension in their role: there could be a certain amount of resentment about being in a subordinate role to a woman, obeying orders in domestic settings, and employers who felt awkward about the situation on their end were known to make them into figures of fun. (Outdoor servants like gardeners, chauffeurs, stable staff, etc. were more secure in their lack of employer supervision and association with typically male tools and work.) Probably the most masculine situation was that of batmen - military valets, basically - who were in a wholly male environment, and they still sometimes felt that their duties made them lesser soldiers. So, while a valet in a single man's household like Jeeves would have the benefit of not being given his orders by a woman, one with less perfect equanimity would still have found himself irritated from time to time, either at the domestic tasks he was expected to undertake or at remarks his employer might make about his ability to do them.

Tensions became particularly prominent when servants recognized that they were superior in some way to their employers - when they were more traveled, or more educated - and when employers could feel that, or noticed/worried that the servants were mocking their foibles below stairs or in corners. This is a recurring issue in the Wooster/Jeeves books: so many situations where Bertie can tell that Jeeves disapproves of his Tyrolean hat or his purple socks and wears them anyway (until Jeeves's plan mysteriously ends up destroying them), telling his valet that he's in charge and will decide what he wears. In real life, the valet would never have been as indispensable as Jeeves and might have been dismissed if his employer felt that his telegraphed disapproval was too obvious.

While the stereotype of the young country lass/boy entering service and remaining there for the rest of their lives does have some truth to it, most servants were gradually introduced to service in their teens by working informally and sporadically for local families closer to their social level, and might hop back and forth between it and e.g. factory work. Typically, though, an upper servant like a valet who was expected to have certain specialized skills (mending, dress sense, French) would make more of a career out of it, working their way up from relatively unskilled positions. Thomas Kilgallon, mentioned above, started out as cook/cabin boy on a sailing boat, as his father was the skipper of the owner's father-in-law's yacht; when Kilgallon senior died suddenly, Thomas was hired by the father-in-law's son - first to do more boat work, and then to take care of personal, valety matters. At times he was sent away for training, and he also assisted other upper male servants in their work. William Henry Clifton likewise joined the Duke of Norfolk's household as a teenager and was promoted to porter and then valet; Charles Smith in the twentieth century started out as hall boy, and then became steward's room footman (a servant to the servants), schoolroom footman, traveling footman, valet, and then butler. Eric Horne, author of What the Butler Winked At, also started out in a junior position, worked his way up to under-butler/footman, and planned to work for some time as a valet in order to see a bit more of the world (valets would travel with their employers) before rising again to the rank of butler. Unlike the others, he did this while switching households in order to find appropriate vacancies.

As far as daily life went, valets spent a lot of time with their employers and in their employers' rooms. In the morning, they would make sure the dressing room was prepared, with wash-water, towels, and shaving and grooming supplies, and set out clothing for the day. After helping the master shave and dress, he'd tidy up the room while the master had breakfast. At night, he'd help him undress and take care of the clothes that had been taken off. He'd polish the shoes, brush off dirt, send things down to be laundered. If the employer went riding or doing some other unusual activity, he'd help him change clothes before and after that as well. When traveling, he'd manage the luggage and tickets. Over the course of an ordinary day, he'd also handle a lot of more general tasks as requested, or at least receive the orders and delegate them to footmen. For more specific descriptions, I'd recommend looking at some of the memoirs I mentioned in my first paragraph, as well as books like The Servant's Guide and Family Manual (1831) and Mrs. Beeton's Book of Household Management.

Further reading:

Lucy Delap, Knowing Their Place: Domestic Service in Twentieth-Century Britain, Oxford University Press (2011)

Jeremy Musson, Up and Down Stairs: The History of the Country House Servant, John Murray (2009)

Sorry if this isn't quite on topic, but the famous Jeeves of P.G. Wodehouse lived in the Edwardian period, post-Victorian. The novels themselves establish Jeeves as a bit of an antiquity by the early twentieth century, and Wodehouse even wrote some later novels in which Jeeves' master Bertie Wooster had to learn to do things like cook for himself as the idea of having a valet became increasingly anachronistic.

Follow up question - how did these people fit into the class structure? They seem unusually well spoken and articulate for someone who is essentially a servant. What kind of education would they have had?