Hi Jürgen,
Thank you for the great question, this is likely useful for many.
Let's start with or. Usually, this operator is the simplest to recognize, you'll find it when using "or" and it is sometimes implied when a choice is given. However, in day-to-day language, it is often confused with xor, the exclusive or. In our course, every time either is used, it is xor, anywhere else, or means or. In real situation, you may have to require your client to specify what is meant.
For the case of "and", while "and" is often used, it is also often implied. For example, in the line "this excellent white shredded French cheese", this cheese is excellent AND white AND shredded AND French. When searching for "and", it's best to think about what is said to be simultaneously true, and put in a conjunction all those statements. When and is not used, synonyms include but, however, along with, plus, also, as a consequence, as well as, furthermore, including, moreover, together with. Note two notable ways to get a negative "and", in the form "not p and not q": "nor" and "neither" are usually used to denote a negative and.
By far, the most difficult operator to recognize is the "implies" operator.
There is p is a sufficient condition for q, p only if q, p implies q, q whenever p, q is a necessary condition for p (i.e., if not q, then not p), or ¬ q→¬ p, q is a consequence of p, q follows from p, q if p, if not q, then not p. See this post. Generally, if you see "if", "implies", you are in a conditional statement. When analyzing conditional, be also careful to determine which is the condition, and which is the implication.
Logic is everywhere, so people have all kinds of ways of expressing their reasoning. Sometimes, it just takes patience.