More on the Conditional Tense   Looking further into the conditional Spanish tense we find that sometimes a past subjunctive verb is called for.  Usually these sentences contain an "if" clause.   If this, then something would happen.  The condition that something would happen is hypothetical.  You may want to look at the articles "On One Condition" and "Past Hopes, Desires, and Uncertainties" for review of the conditional and the past subjunctive tenses.  This article kind of ties these two tenses together.   Let's first look at two examples of the conditional tense with no call for a subjunctive verb.   I would eat the cake, but I'm on a diet. - Comería la torta, pero estoy a dieta.   They would not live in that house because it's too old. - No vivirían en esa casa porque está demasiada vieja.

No subjunctive verbs are required above because the conditions that I am on a diet, and the house is old are factual statements and not hypothetical.
Now take a look at some conditional sentences where the conditions are hypothetical:
I would play basketball if I were taller. - Jurgaría balconcesto si fuera más alto.
If you knew the answer, would you tell it to me? - ¿Si supiera la respuesta, me la diría?
'If' I were taller, and 'if' I knew the answer, are hypothetical conditions that trigger the past subjunctive.  
Let us look at a few more:
I would not go if I were you. - No iría si yo fuera usted.
You would speak Spanish well if you studied. - Hablaría(s) español bien, si estudiara(s).
Would you stay if the hotel were free? - ¿Se quedaría si el hotel fuera gratis?
If it were not so cold, I would play tennis. - Si no hiciera tanto frio, jugaría tenis.  
If it were not raining, we (would) could play golf. - Si no lloviera, jugaríamos golf.
All the conditions are hypothetical and call for a past subjunctive verb.  
Now here is a rather odd condition in which the past subjunctive is used with the conditional tense.  Look at how gustar is used here.
I would like you to teach me some Spanish. - Me gustaría que me enseñara algo de español.  
To me this looks like a straight present subjunctive sentence.  Not past subjunctive (eseñara).  I am desiring for you to teach me some Spanish.  Nothing here about the past.  Yet the past subjunctive is used.  Sometimes it's hard to explain why certain Spanish sentences are the way they are, especially when the subjunctive is involved.  We just have to accept and memorize them.
Learn and practice the conditional tense with and without hypothetical conditions and you will be speaking Spanish much better.  Look for opportunity to practice in live conversation- always!
Hope this helps,