There's something called structure activity relationship (vaguely, because there's a lot of subdivisions), that explains/predicts how certain patterns of structures and pharmacophores bind to certain receptors and proteins. By knowing the physiology behind certain disorders, what genes, receptors, proteins and celular structures they affect, you have some theoretical targets that holds some potential for being where a drug will have it's mechanism of action interfering with.

After some ligands to some targets are known, you may use them as skeletons to serve as a base. By making some changes in specific places, for example, you'll have changes on how fast they're metabolized, how well absorbed they re through a route of administration, how potent they are and wether they are agonists (i.e. they activate the receptor), antagonist (they bind to the receptor without activating, preventing other ligands to bind and activate), inverse agonists (simplifying it, they bind and cause a "reverse" signaling). If the target is an enzyme, it could be an inhibitor or an inducer. Overall, such small changes with new ligands called radicals produces analogues of the drugs and the molecules are then studied individually to see which of them do the best job to a purpose. Often, some discoveries may happen to be accidental too, by screening the biological activity of a molecule for a purpose and later, on pre clinical studies, clinical trials or even post-market, it's found out that they are also useful for something.

It's kinda hard to simplify every possible process, especially because I mainly study the design of new psychoactive substances and that's a very specific case.

An example could be a drug used to treat high blood pressure. Take propranolol or atenolol for example. It was known that the activation of noradrenergic beta receptors increase blood pressure, then, having something that blocks it, i.e. a beta blocker, will prevent endogenous sympathetic stimulation to activate them. If you look at both molecules, you'll see the similarities. See also salbutamol molecule and compare it to adrenaline and noradrenaline. It's basically an analogue which activates beta 2 adrenergic receptors.

Edit: I feel like I've oversimplified too much. If you're interested on structure activity relationship it, you can have some fun by playing a little bit with swisstargetprediction.ch and put a molecule on it, then make a little change here and there and checking which kind of ligand do something. It's a good starting point for learning and for fun.