In general, the actual winemaking process for Kosher wines is the same as most other wine. However, there are a few rules to which Kosher wine must adhere.
First, Kosher wines--especially wines that are Kosher for Passover--are not allowed to come in contact with any grains, bread or dough. These items are not typical in winemaking so observing that part is pretty easy. Second, wines cannot have animal-based additives. While this sounds odd, things like egg whites and gelatin are used to remove excess sediment from a wine before it is bottled. Wines marked as “vegan” do not use animal-based products for this process and Kosher wines are great options for vegans as well. Finally, for a wine to be considered "Kosher," the entire winemaking process must be at least overseen, if not entirely performed by Orthodox Jews.
Once the Kosher wine has been bottled and sealed, the unopened bottle is allowed to be handled by anyone. When the bottle is opened for serving, it again must be handled only by Orthodox Jews, unless the wine is “Mevushal” (me-voo-shal). Mevushals are wines that have been flash pasteurized, thereby allowing them to be handled by non-observant Jews. This is an option preferred by restaurants and caterers, however the heat of flash pasteurization does have a slight impact on the taste and texture of the wine (wines generally don’t like heat!).
If you aren’t as concerned with strict rules and don’t want a wine that has been exposed to heat but still want something special for Passover, the Pianetta Merlot may be an acceptable compromise. The wine has been blessed by the Kiddush prayer by a Rabbi.