Most medieval people probably had little experience of voting, except perhaps very informally. Urban populations did sometimes have elected councils or leaders of some type, often chosen by fairly complex systems. The election system in Venice, as I recall, involved several alternations of choosing candidates by lot and then voting from among them, or voting on a pool of candidates and then choosing one of them by lot, and so forth.
Medieval nuns and other religious did have opportunities to vote. Abbots and abbesses, priors and prioresses were often elected by the monks or nuns or canons they were supposed to lead. Since they were then elected for life, individual nuns / monks / canons might not have had very many opportunities to vote in their lifetimes.
The Rule of St. Benedict says briefly that the abbot should be chosen "either by the whole community acting unanimously in the fear of God, or by some part of the community, no matter how small, which possesses sounder judgment." (RSB 64:1, in the 1982 edition from The Liturgical Press, Collegeville, Minn.) Unanimous choice of an abbot or abbess was probably fairly uncommon. How did this "some part of the community" method work out in practice?
In 1283 the abbess of a small Benedictine nunnery in Catalonia died. Shortly after, the prioress convened the nuns. The twenty nuns present chose three of their number as a commission and agreed to abide by their decision. They therefore acknowledged those three as possessing sound judgment and being worthy of the community's trust. All three were venerable women; two had been nuns for at least 35 years, and the remaining one had been a nun for at least 27 years. Probably all three were at least in their 40s or 50s then, and possibly were considerably older. In addition, these three nuns had an advisor: the abbot of a nearby community of Benedictine monks. These four people deliberated for a time--not more than a few hours, in this case--and then announced their decision. They chose as the new abbess the community's prioress, a woman who had held the offices of prioress and infirmarian in the nunnery for 20 years. They praised her learning, prudence, and discretion, and their choice was attested by all those present. The witnesses included not just the twenty nuns of the community, but also its chaplain as well as representatives from the local cathedral and other men's communities.
This election went very smoothly: a well-qualified candidate was available and the chosen delegation came to agreement quite easily. Certainly not all medieval religious elections went so well, but this example must be practically the ideal.
Incidentally, the Catalan scholar Ramon Llull seems to have been interested in voting (among his many other interests) and proposed some much more elaborate schemes for conducting elections; I found some discussion of this methods here.