First off, to be clear, this is a review of the cellar tour, NOT the cafe; that's another review…read more
That being said, Veuve Clicquot is a massive champagne winery with a fascinating backstory. I won't get into that here, but, if you take a winery tour, you will hear about it. There's actually a movie on Netflix detailing it as well, but the winery points out what they got wrong.
Anyway, this place is easy to get to, either from Reims itself, or on a day trip from Paris. From Paris, you could take a bus, or take the TGV (45 minutes to an hour), from Gare de l'Est (be sure to validate your ticket before you board!). If traveling locally, if you have a vehicle, they have lots of parking in their lot across the street.
Once you arrive, check in at the front desk, then they will direct you where to go. Be on time - seriously, you're super rude for something like this if you're late. They will try to accommodate you if you are, but just plan extra time. Anyway, where you go after checking in depends on which tour you booked, and there are several options. Your level of booking will impact the champagne you taste at the end, but my guess is the tour is relatively the same regardless. You start the tour with a quick video and intro to the tour guide, then it's off to the cellars.
The cellars are actually crayeurs, or old chalk mines from way back. These cellars are deep, hence dark and cool, which makes them ideal for making champagne. While on the tour, they'll discuss the history, the technology, the craft, and so on, all in different chambers of the crayeur. Interestingly, Veuve Clicquot actually invented a technique that revolutionized champagne making at the time, a process that is still done today (though via much more modern methods). They do two to three tours at a time, so if one crowd gets rowdy, I can see how that would get loud, as others have said in other reviews, but it was not an issue on my tour. The culmination of the tour, and probably also the loudest part, is the tasting. Again, depending on what you booked, you will have varying levels of quality. This part is particularly fun, and the tastings are delicious! They provide lots of detail about the wine, how it's aged, its flavor, and so on. It's very interesting, and even more so if you're a fan of the brand.
After the tasting, you return back to the main building, though a different entrance than you left. They do have a boutique with lots of great items, including some famous vintages (such as 2015), so it's definitely worth taking a look. If you feel so inclined, grab a bottle of La Grand Dame, then hit up the cafe outside (which is a different review).
Overall, this place is really quite amazing, and they've got things organized incredibly well. If you can only choose one or two tastings in your time here, this would be a solid one to choose.