In some respects, the Middle Ages were a rather clean era; the Roman bathing culture survived well into the 14th century and public saunas were commonplace everywhere in Europe. In rural areas away from the urban centers, people bathed regularly in ponds or streams.
It was The Black Death (ironically) that signaled the death of this bathing culture: fear of pestilence closed the public baths and had a detrimental effect on social conventions, like changing one's clothing regularly and concern about body odor. Rudimentary scientific thought added to it, as people noted that going to bathhouses was often an instant Black Death contagion, which instated the idea that being less clean was a small price to be alive. The closing of bathhouses also caused that many people who couldn't otherwise afford to bathe at home (this required a lot of water, fire and time) were left without any more option that wash themselves by body parts whenever they could, and to use plenty of perfumes and cosmetics to mask it.
This led to the genuinely filthy hygiene of the Renaissance and the centuries following it: the spread of plague, syphilis, and the end of the Medieval Warm Period effectively killed the sauna culture everywhere in Europe outside the regions where it was practically a winter survival technique — Scandinavia, mountainous areas, the Polish-Lithuanian Commonwealth and Russia. Europe really recovered only with the spread of the modern sanitation in the 19th century, although bathing (now private rather than communal) at least made a comeback during the reign of the obsessively fastidious Louis XIV, who was ironically infamous for never bathing himself. For a while, it was even fashionable for wealthy ladies to have their portraits painted in the bath.
Similarly, dental hygiene had been a common practice for thousands of years by this point, and continued to be so — it's not difficult to make the connection between cleaning one's teeth regularly and avoiding bad breath and painful tartar buildup. While proper bristled toothbrushes would take time to spread beyond Central Asia, they were invented in this time period, and the basic concept of scrubbing and picking one's teeth with a stiff feather or frayed stick is mentioned as far back as Mesopotamian writings. Additionally, the sugar- and acid-related dental problems of our times were almost unheard-of, cavities being mostly the worry of elders whose enamel had been worn down over decades by the grit from stone-ground grain and flour. Again, it was during the Renaissance, when sugar and flavorful acidic foods moved from exotic luxuries to common fare, that teeth became an endangered species among the major world trade powers of the day. Dentistry was surprisingly advanced by this point, but again, it was something that required a lot of money.
Another common misunderstanding is the era's typical lifespan being in the mid-30s. The average life expectancy was, but it was skewed downward by the high rate of infant and child mortality, as well as by the high percentage of mothers dying in childbirth. If you managed to survive your childhood and childbearing years, you had a fair chance of living into your 50s or 60s if not higher. Even many centuries before the Middle Ages even started, reaching the age of seventy may have been considered something of a standard, witness the Bible (Ps 90:10): "The years of our life are seventy, or even by reason of strength eighty". You can also note how, in the story of Ancient Greece, Rome and China, people with jobs comfortable and not directly related to the possibility of being hacked down to death every day, like philosophers and statesmen, routinely reached ages we would find perfectly normal today.
The dung, however, was absolutely real — in cities, at least. Remember that the overwhelming majority of the population was rural. Most medieval cities had a "Shit Creek" or something similarly named, where all the sewage and waste flowed to and was dumped, and the unbearable foulness of such cesspools was well-documented. Likewise, with no underground sewers, human waste was, at best, collected in open-air sewage canals, and at worst dumped into the street. Similarly, pack animals were necessary for moving goods through the city, and urine and manure of horses and other ungulates was certainly common on the unpaved streets. Obviously, this was much worse in the poorer, more densely populated areas of the cities, and these poor sanitation conditions contributed greatly to recurring disease in the Middle Ages. Pit latrines were possible to dig, but those of course filled up sooner or later, necessitating that they be emptied — as in, someone had to go in there with a shovel and bucket and clean them out.note Animal dung could be used for agricultural purpose, however.
In terms of smell, in a relatively clean city that enjoyed good weather, you could probably expect something like a barnyard. It's hardly impossible to adjust to and become comfortable with a barnyard odor, so people in such cities probably weren't especially bothered by it. If the city was not so fortunate, or if conditions had declined, a sewer-ish smell of rot and decay was definitely possible and, as you might imagine, widely lamented.
