What determines gender in to whom one is speaking?
The first example below ,le dije , 1st person preterite ,I said to him ,or told him.
This is understandable and self explanatory, but not the one below .
2 nd example ,le dijo, 3rd person preterite, she asked , or she said , what has
determined that it is she , why not he asked ? forgive me for being thick,
but I cannot find an explanation anywhere.
These are examples from the word of the day in the dictionary.
lo hizo al revés de como le dije -> he did the opposite of what I told him to
Lo hizo al revés de como le dijo. - He did the opposite of what she asked.
9 Answers
The first example below ,le dije , 1st person preterite ,I said to him ,or told him.
The pronoun "le" does not specify gender; it could be "him", "her", and even "it".
Le dije algo a María -> her
Le dije algo a Carlos -> him
Le puse sal al arroz -> it
2 nd example ,le dijo, 2nd person preterite, she asked , or she said , what has determined that it is she , why not he asked ? forgive me for being thick,
A sentence like "Le dijo algo" is never uttered out of the blue, without context, because if someone did, you would end up with four different translations in English:
He said something to him
He said something to her
She said something to him
She said something to her
But again, no one dials someone's phone number and simply says "Le dijo algo" right away, without a "Hello!" first. In practice, those pronouns will be used in a situation or a conversation that will allow you to determine unequivocally who talked to whom. When you say in English "I invite you", do you mean "Te invito" (to one person) or "Les invito" (to more than one)? Because you can't translate that sentence into Spanish unless you know whether you mean "you" for one, or "you guys" for several, but the context normally provides this information. The same goes for "I saw them": did you see women? Men? Or both?
lo hizo al revés de como le dije -> he did the opposite of what I told him to
They have chosen "he" at random, because it could have been "she" as well. That's the problem when you translate sentences devoid of any context: you have to make random choices when contextual information is missing and the other language's morphology demands a distinction that the other language does not express formally.
Lo hizo al revés de como le dijo. - He did the opposite of what she asked.
Same thing: it could have been a "she".
When you say in English "I invite you", do you mean "Te invito" (to one person) or "Les invito" (to two people), because you can't translate that sentence into Spanish unless you know whether you mean "you" for one, or "you guys" for several.
Not only does standard (modern) English fail to indicate number in this case but it also does not indicate the sex of the person(s) spoken to. Arabic, on the other hand has masculine and feminine (as well as singular/plural) forms for the 2nd person pronoun. American feminists who are so concerned about the gender bias represented by English grammar would, no doubt, hail this as evidence of the sensitivity displayed by men in the Arab-speaking world toward their womenfolk.
Yes, it is not very clear:
Lo hizo al revés de como le dijo.
This could mean:
He did the opposite of what she asked.
-He did the opposite of what he asked.
-He did the opposite of what you (formal) asked.
Hope this helps mate. Good to see you by. 
to avoid ambiguity in the following sentence =
Lo hizo al revés de como le dijo. - He did the opposite of what she asked.
It could mean he / she asked therefore one could insert a personal pronoun ,
Not really, ray. Here we are talking about a random sentence, but in a normal conversation or text, context would make this perfectly clear. Only when this is not the case, would we use a personal pronoun.
Thank you for all these wonderful answers which have made me realise that
I am not overly thick. Although I would like to see in future the dictionary saying ,
to avoid ambiguity in the following sentence =
Lo hizo al revés de como le dijo. - He did the opposite of what she asked.
It could mean he / she asked therefore one could insert a personal pronoun ,
Each answer was thorough and beneficial making it hard to accept one as being better than another .
Only context could tell you.
For example, let's say the whole conversation was as follows:
María mandó a Juan limpiar el baño, pero lo hizo al revés de como le dijo. Lo hizo más sucio.
(Translation: Maria told Juan to clean the bathroom, but he did the opposite of what she said. He made it dirtier.)
Now it's completely clear that dijo is "she said" and not "he said" because Maria is the one giving orders (saying stuff) and Juan is the one doing stuff.
How did you know that it wasn't it said? Gramatically that is a possibility, but common sense tells you that "it" normally does not speak (except ocassionally in children's stories). So, from context you rule out the "it"possibility which you would not do if the verb were, for example, to fall (caer). We often have to glean the subject from context.
Despite the "rule" here on this site that subject pronouns be avoided, this is exactly the situation where they are used to avoid ambiguity. Forget about explaining to whom it is being said. Use a subject pronoun to express the speaker subject (él o ella) if there is no context to tell you who said it.
Él lo hizo al revés de como ella le dijo.
You question is worded a bit confusingly. It asks about how to clarify to whom [le, the i.o.] the sentence is speaking, but then you examples and description talk about determining who is speaking (the subject). Is it él or ella dijo/hizo?
lo hizo al revés de como le dije -> he did the opposite of what I told him to
Lo hizo al revés de como le dijo. - He did the opposite of what she asked.
The 2nd sentence does not follow the paradigm:
1st sentence ...he did the opposite of what I told him
2nd sentence...he did the opposite of what I told her
This would examplify the ambiguity surrounding le. The given examples swtich from the ambiguity of le to the ambiguity of dijo. (at least, the English part does)
[Also how the English verb "asked" got involved in the translations eludes me. I see neither pedir nor preguntar in the Spanish.]
As said above, it remains ambiguous unless the context makes it obvious or more commonly, a él, a ella, o a [Name] is used to clarify. The one thing that I wanted to add and although not grammatically correct I suppose, I find it extremely common where I live.
Le dije ---> La dije ---> I told her Le dije ---> Lo dije ---> I told him
While incorrect, it has been adapted by literally everywhere that I know and I now find myself using it just because it is faster and clearer. I've always thought language is constantly changing but if you don't like it, at least you'll be familiar with it if you hear it.
There's no way to tell from just le dijo whether it's a he or a she that was spoken to, but usually this is clear from the context of the story. If this is not the case and it's still important know that it was said to the woman then you should add a ella or a Maria (if that's her name) to avoid ambiguity.
Le dijo a ella - You (formal) told her
