We can give you only partial clarity – and an assurance that there are many legitimate ways to fulfill the minhag.
The minhag to eat milchig food on Shavuot seems to have begun in Ashkenazic lands in the days of the Rishonim, and it is accepted by the Rama.[1] However, over time it has become a more accepted practice among Sephardim, as well.[2] There are many theories as to the rationale behind the minhag, which affect the optimal way to follow it. Also, some ostensibly good ways of fulfilling this minhag raise halachic problems. Given the plethora of opinions on the matter and the fact that people recognize that this minhag is not overly crucial, it is not surprising that both rabbis and laymen have developed varied systems.
The Rama[3] understands that the minhag is meant to remind us of the shtei halechem (two loaves of bread), which were offered on Shavuot in the Beit HaMikdash. The Magen Avraham[4] explains that by having both milk and meat products in a meal, it will be necessary to have two loaves of bread with which to eat the food.[5] For that reason, he suggests that we bake some milchig bread. Although bread is supposed to be pareve, loaves that are small or are made in a special shape, both of which were customary on Shavuot, are permitted.[6] This approach explains why many eat milchig and fleishig at the same meal despite the problems that this entails (see below), as the halachic tension it creates is part of the observance.
Another reason to split a meal into milchig and fleishig parts is that many authorities require a meat meal both at night and during the day of Yom Tov.[7] Others say it is sufficient to have meat during the day. Therefore, those who have one fully milchig meal on Shavuot usually do so at night.[8]
Other reasons for the minhag are based on kabbalistic ideas regarding milk,[9] hints derived from the word as an acronym,[10] and the idea that after receiving the Torah, Bnei Yisrael needed time to be able to prepare kosher meat and therefore had to eat dairy.[11] According to these approaches, it may be sufficient to have milchig food at any point during Yom Tov, including a snack or kiddush after Shacharit.
Clearly, one should not compromise the laws of meat and milk in order to fulfill this minhag. Therefore, if eaten in succession, milchig must be first. In between the two parts of the meal, one should clean his mouth by eating pareve food and by drinking or rinsing, and he should also either rinse or inspect his hands.[12] He should also change the tablecloth.[13] (Many people simply eat the milchig food on a plastic tablecloth on top of the regular one.) Some people are careful to make a full break between the milchig and fleishig parts of the meal through Birkat HaMazon (or a beracha acharona in the case of those who fulfill the minhag with cake).[14] However, that is a particularly stringent practice and is not halachically required.[15] If one does bentch, note that there are varied opinions as to how long to wait before starting the meat meal.
In brief, it is all but impossible to coordinate the most stringent approach to the integration of milk into a meat meal on Shavuot with all the stringencies involved with eating milk and meat in general.[16] Some systems are so cumbersome that they might have a negative effect on people’s simchat Yom Tov, cause them to make mistakes, or unnecessarily delay the minhag of learning all night. Therefore, people should continue a family minhag with which they are comfortable or adopt one that works for them. One who wants to figure out the most machmir system may be blessed, but he should be aware of “collateral damage.”