"Trains are big."
it's です because i-adjectives are already a predicate in the sentence. The です function in this case is not a grammatical one, is to change the sentence into a softer tone. This is an exception in the general grammar.
電車は大きい (casual); 電車は大きいです (more polite). ―"trains ar big".
電車は大きいだ would be ungrammatical given the redundancy. ―"trains are are big".
Also, you only use ～ます after a verb, in those cases the auxiliary ～ます is very similar to the です from this sentence, is there as a deferential ender, ～ます alone doesn't mean anything, it only means something with a verb.
効率を上げる (casual); 効率を上げます (more polite). ―"To increase efficiency".
There are no articles in Japanese
は is the topic particle. The topic is sometimes the subject, but not always. This particle marks what the overall sentence will be talking about. It is contextual (old) information that is already known by the speaker. When you see it you can read it as "On the topic of..." or "As for..."
So "On the topic of trains, they are big" or "On the topic of the train, it is big". The exact translation would depend on context; the use of the topic particle just means that "train" is already understood through context, so it was either previously brought up in the conversation or is clearly understood already based on the setting (if you were at a train station or on a train).
If you wanted to be specific about what train you are referring to if it is unclear from context you could say この電車 this train、or その電車 that train
が is the new information particle, and more commonly referred to as a subject particle. It marks the do-er or be-er in a sentence. It puts an emphasis on the word that comes before it.
電車は大きいです - Trains are big [on the topic of trains - they are big] - Trains are known information, 'big' is new information. You are probably commenting on something already mentioned or is visible to the listener.
電車が大きいです - Trains are big [Trains (are the thing that are) - big] - Trains is new information. You are starting the conversation about trains without earlier context.