A holy well may not be a properly built well at all - most of the time it is a spring, often enclosed (and sometimes covered) by more or less ornate architectural additions, revered either in a Pagan or Christian context. At times these contexts coexist or even intermingle. And most of the time it remains unclear whether a certain holy well had already been revered in Pagan times and then been adopted (or adapted) into Christian belief systems.
Size seems to be important - holy wells can range from a trickling spring to a sizeable pool, but lakes and streams are never assumed to be "holy wells". While the term "well" is misleading too - it may hark back to Anglo-Saxon times and the word "haeligewielle", literally a "holy spring", but pronounced all to similar to "holy well".
Holy wells are mainly a part of local belief systems and folklore - through an associated legend (often involving one of the major saints like Patrick or Brigid and implying, thereby at the same time confirming, his or her local presence ... though this may historically be as far-fetched as one can imagine) and through local lore. This local lore may also tie the well or spring to a supernatural entity, a local spirit or even a pre-Christian deity. Rituals connected to the well may reflect the lore surrounding these saints, spirits and deities. Often special feast days are also attached to the well lore - the dates of annual pilgrimages (which, if the holy well is connected to a saint, often do not coincide with the regular feast days of the saint) or of special activities involving the holy well (like well-dressing, which is popular in some areas).
Though the local folklore surrounding the holy well can be very elaborate and comprehensive, the actual development of its "holyness" (sanctity) is often shrouded in mystery. Many Christian legends insist that the water only started to flow through the action or wish of a saint, raising wells or rather creating springs is a common element in the hagiography of the "Celtic" saints. Often out of pure necessity: Patrick was thirsty or had a thirsty congregation, so tap-tap-tap on a stone and fresh water flows. Sceptics may argue that Ireland must have been a very dry place before the saints started tapping - but that would be beside the point. Springs were already venerated in pre-Christian times and the bible gave importance to the instant supply of clean water (necessary for survival in the area) through the stories of Moses. Thus a holy well should be seen as an integral part of Pagan and Christian beliefs, not as a geological impossibility.
Holy wells became extremely popular during the middle ages and acquired often miraculous properties, if not in official ecclesiastical documents, then in folklore - though the Reformation tried to stamp out these practices, parts are still alive in local lore. Thus you may find reference to the waters being beneficial against all sorts of diseases, with some more specific than others. These beliefs are still held in high regard in some areas, with the advice to drink the waters, which has led to the rather confusing practice by local councils to erect large signs warning against the same for reasons of health and safety ...
After the Reformation, holy wells were "re-discovered" by folklorists and antiquarians, mainly on the British Isles during the 19th century. While Philip Dixon Hardy composed his "Holy Wells of Ireland" (1836) as a rational Protestant attack on irrational Catholic traditions, later years saw a more balanced, non-partisan approach. Robert Charles Hope published his "The Legendary Lore of the Holy Wells of England" (1893) as a non-judgemental general survey and included wells with no Christian connection at all. Restoration of holy wells, often in a rather fanciful way, was also becoming popular around this time - though more than often they were regarded as scenic features more than sacred places.
Apart from local folklore and beliefs, a resurgence of interest in holy wells came with the Neo-Pagan movements during the 20th century. Here the pre-Christian and Celtic origin of holy wells was often emphasized, though this emphasis nearly as often lacked any evidence. There have been numerous books and articles published on holy wells in recent years, often with wildly contrasting viewpoints, more than often due to an approach to the local folklore that tries to fit it into a global belief system.
The easiest way to locate a holy well when travelling Ireland is to simply look on a map - the large scale maps sold by Ordnance Survey Ireland often mark these places (though access might not be that easy). Holy wells are also often found sign-posted locally, though this can be "very local" at times (like a large sign in the middle of a cemetery, but no sign leading you actually to the cemetery). You will also often notice offerings left at holy wells, respect these and never take them as quaint souvenirs.