This is a fairly complex topic and even the experts disagree on the nuances. The web has vast amounts of information on the formation and use of the conditional/subjunctive, the decline of the subjunctive in English, and provides many examples.
The conditional mood involves statements in which the results or outcome are contingent (depend) on a given situation or condition, including, like the subjunctive, hypothetical situations. The certainty of the outcome can vary from absolutely certain (not always considered the "true" conditional) through generally, potentially, and rarely certain to contrary to fact (the unreal conditional). For example:
If you take LSD you start to hallucinate. (Certain)
When I feed my dog, he usually bites me. (Generally certain)
If he were to arrive right now, we might have a chance to see him. (Hypothetical/uncertain).
If I made lots of money, I would invest in gold (Contrary to fact).
The subjunctive mood treats statements of emotion, wishing, uncertainty, and contrary to fact/hypothetical situations:
I wish he were dead!
May you always be prosperous!
I wish I were in Figi, it is too cold here.
Would that it were true!
There is a link between the conditional and subjunctive: in an unreal present conditional statement (one hypothetical or contrary to fact), the main clause (the result) is in the conditional while the subordinate clause (the condition) is in the subjunctive:
I would have more fun in Berlin if I spoke German. (I don't speak German).