I read that the second thermodynamic law says that entropy in an isolated system always increases with time. That is okay, but how does this apply to energy transforming devices and other systems that are not isolated? Is there maybe a better saying of this law that is broader? My understanding is that whenever we have energy conversion, there is some entropy increase and thus some loss of useful energy, but I don't see how that connects to the saying of the second law above.
Every system, be it isolated or not can actually be encompassed with the definition given above. Before explaining that let me just say this, there are thousands of ways you can state 2nd law of thermodynamics and each of them will lead to others as some corollary.
So, you started with "Entropy of an isolated system always increases or remains the same. It always increases for a irreversible process. Now if you have a non-isolated system you can consider the universe (=system + environment) to be an isolated system. In this system your law holds. Thus when a non-isolated energy converter takes energy from a environment it cannot do so without spending some energy as heat. Because the total system(the converter+the reservoir or source) must increase the entropy. Thus your first version of the law also ultimately gives the conclusion you were looking for.