Bargain Directly With Hotels: By far, the most significant cost of a tour is lodging and hotel owners are willing to negotiate. How do I know this? It is the first time in years that hotel owners have been calling ME asking to book clients, therefore, I am going to assume that hotel occupancy rates are down, especially in Europe and South America. It is possible to negotiate on price, including special offers like upgraded rooms, breakfast, or extended check out times. The consumer has more leverage now than I have seen in a long time.
Bargain Directly Apartment Owners: I always found apartment owners were negotiable, especially in off-season. This is how I negotiate on an apartment I am looking at with a listed price of let's say 200 euro a night: the first thing I do is put into my head a price I want to pay for the apartment and let's say that is 165 euros per night. I will first make an offer of 130 euros per night expecting a counter-offer. If they meet my goal of 165 euros a night, I take it of course, otherwise I will move on.
Admission to Attractions: In most European cities, the cost of admission to museums and attractions is relatively low. For instance, in Paris the Louvre is about 15 euro. The Orsay is 12 euro, Rodin Museum is 10 euro and the Pompidou is 14 euro. However, a Paris Museum Pass with 4 full days of unlimited, no-wait-in-line admission to all of these sites plus about 45 more is only 62 euro. The bargain is not in the price, but in the time saved of not having to wait in line. Most European cities have a museum card similar to the Paris Musuem Pass.
Trains: Simple - buy tickets in advance. I use a great app and website called Captain Train as a one-stop place to buy all my Europe train tickets.
Airfare: This is probably the second costliest expense of an overseas tour. My advice is simple: buy tickets 2-3 months in advance and look at blog posts I have posted previously on saving on airfare.