Proximity. Speaking only for the Medievals, they did understand that separating wastewater from good water is important. Taking the case of Medieval London, the 'necessary houses' (public toilets) were either along the city wall or the Thames. Those on the wall drained the effluent into the moat, or the Walbrook stream.

City laws also ruled the placement of cesspits in London. Unlined cesspits must be at least 3 and a half feet away from the property line, while stone-lined cesspits are allowed from 2 and a half feet away from the line. Complaints about cesspit placement were frequent, however. Some latrines could also get elaborate. Some were lined with barrel staves, others with stone; still others had a pipe to convey waste to a more distant cesspit.

Alternatively, they'd draw their water from elsewhere. Medieval aqueducts drew from springs some distance from the town, which would be much less likely to have any cesspits nearby. I have a post with more on aqueducts.

Alternatively alternatively, they'd use rainwater. While the Medievals did not have germ theory, they did have an understanding of cleanliness and contamination. Multiple sources from multiple places and multiple times caution about using stagnant water, still water, or otherwise water that does not flow freely. Rainwater, being by definition none of the above, places high in many rankings of water from the ancient to the Medieval. Rainwater can be collected by the simple expedient of a bucket or barrel, or you can do more elaborate arrangements. Solid roofs and pavements can be connected by gutters to a cistern (if you have the money for all of the above, of course) and thus collect rainwater thereby.

Of course, sometimes the answer is simply "they didn't". Elena Gubbe in 1324 and a nine-year-old named Mary in 1340 both drowned in the Thames while drawing water in the evening. The Thames, of all rivers. (Though it is possible they were upriver of the worst contamination - who knows.)