I'm a pharmacy student and I can try to explain how they do to find new drugs.
In fact, there are many diferent ways to do so, it depends of what kind of new drug you are searching for.
Sometimes you're working on a disease which the pathological molecular mechanism of action are well-known and where many drugs are already effective. In this case, the 'assay' may just be about improving a well-known molecule by adding or changing a small part of the molecule (replace a ketone by an alcohol for exemple). Always in this case, you know on what molecular receptor you have to act, its 3D structure, its composition, its location in the human body and maybe the most important (but you don't know this every time and in this case, you could begin by this point) how and what part of your drug acts on any part of the receptor.
Then you have molecular libraries where you can search your new drug. They are alimented by different ways: someone who found a new chemical reaction that can add a chemical function where you could not before and generate several new compounds by applying his new method. All this compounds can be given to a national library where access is possible. You can also find intermediate compounds of reaction. This happens in public research because private laboratories keep their discoveries secret.
Sometimes you're working on a disease where the usual drug doesn't match really with the receptor, in this case, you have 3D tools that can modelize molecule and receptor in order to quantify how they match. This is achieved on many many molecule from this library and these methods generate few drugs that match the best.
Then you work on these drugs to improve them and make them compatible whith digestive barriers if you want an oral drug, or with the galenic form you need. This point is about improving the matching with the receptor by changing few parts of the molecule.
In fact when you know on which molecule you want to act, it all start with IT tools that mesure interactions between this molecule you want to act on and other random molecules.
When you don't know molecular mechanisms of your disease, you have to find it before, otherwise you're gonna work double-blind.
This is a few part of the reality, I hope that answered the last part of your question.