How to work in costume
A good costumier can look at any production and tell you exactly when it is set based on the actors' apparel alone.
An overview of the history of clothing is an extremely useful thing for anyone who works in the costume industry; you need to know your doublet from your dinner jacket if you are going to convincingly place your character within their setting. This is something that will be taught on any good costume course, and there are some excellent books out there on the subject.
It is also useful for the costume professional to have some background knowledge of the historical context of the characters that they are designing for. It would be difficult to design for 1940s England without taking the influence of WW2 into account (just one example being the restrictions on certain fabrics due to rationing). Similarly, if you are designing for characters in 18th century France, you need to know whether they kept their heads come the revolution. For period productions in particular, it is difficult to get under the skin of the character without a basic understanding of the history surrounding them and the social and political events in the time that they lived in.
However, a key part of working in costume design is research. Even the most experienced designer will do additional research into the specific period of a film or production. They will look for visual reference in the aforementioned books and also through paintings from the time and museum exhibits. They will also look at context and consider the socio-economic status of the characters, and use all this information to create a defined picture of the world in which the characters live. You don't have to know absolutely everything there is to know about the period you are costuming for before you begin, but by the time you start to draw up your designs you should ideally have a good idea of how your characters lived and therefore how they dressed.
As you progress through your costume career you will build up a stronger mental database of the various historical periods, and the whole process will become easier as you are able to find links and make connections to other productions. In fact it is always a good idea to keep a file containing your research from each production which you can continue to add to, creating your own personal history resource book over time. You will eventually create a clear visual timeline in your mind, and then you too can impress/annoy your friends by pointing out the year that costume drama is set in.