Hi! I saw this was a repost, so I wanted to pitch in. For my time and place of study (northern Europe, 700-900), there's not much information on the wedding ceremony itself (at least not much evidence that I've seen). Weddings were looked upon as a predominantly religious event, so ideally a priest would have to preside and most marriages probably took place in churches. This is before the theology of sacraments was fully developed, and since there's no clear biblical template (like there is, for example, for baptism), we can anticipate that things could have been done very differently in different times and places. But aside from the ceremony, there must have been feasting. Feasting was a critical dimension of almost every formal event in early medieval societies, and so just like many marriages today, what happened at the wedding reception was probably often more important than the wedding itself.

Early medieval law codes do include provisions about slaves running away to a church to get married, which tells us at least three really important things: (1) marriage wasn't restricted to the freeborn and wealthy, (2) some people got married because they wanted to, and presumably at least some couples were motivated by love and affection rather than pragmatic concerns about property and inheritance, and (3) most people—male or female—who had a master, lord, patron, or other guardian needed to get permission to get married, and if they didn't get permission, both the couple and the priest who married them might be considered culpable (although it's unclear whether this would mean that the marriage would be dissolved).

That said, there were also many times when people would cohabitate without being married. We actually have few clues about how "Christianized" the average peasant would have been throughout much of the middle ages, but I think it's a safe assumption that many (at least until churchmen started stressing the sacraments around the 1200s or so) lived together with what we might term common-law marriages, without there ever having been an official ceremony or maybe just a sort of housewarming banquet when a couple moved in together or took over the family farm. Among the elite, however, cohabitation among free men and women was probably very limited due to potential inheritance disputes. Many men nevertheless took concubines. For example, Charlemagne had at least five that we know of, and there seems to have been no ceremony at all associated with taking a concubine. In some very rare cases, even among royalty, it seems like concubines gradually became accepted as full wives, most notably including the Merovingian Queen Fredegund. The stories that survive about Fredegund don't suggest that there was ever a wedding ceremony to mark this transition.

If you're interested in another place or time, or if this post doesn't get the responses you're looking for, you might try reposting it with some more specificity, which gives potential respondents a bit more traction. For example, "What were weddings like in late medieval England?" or "What are some good descriptions of weddings in the Middle Ages?" Hope that helps!