Without seeing the actual text of the sentence you mention having seen, and probably also its surrounding context, it is impossible to say for certain. In the edited text on the bottom, I posit a couple of ways in which it would be acceptable in Standard English.
However, in the most common way of constructing it, when it is an actual conditional and not a permission thing, then
- If X would do this, then Y would do that.
is not considered Standard English. You often hear it in non-native speakers — and perhaps more commonly from those non-native speakers who originally have a Germanic language as their first language. I’m speaking only from experience on that hunch, not from research.
Nevertheless, you also sometimes hear this would–would conditional construction from native speakers, too. It still is not considered Standard English. An English composition teacher, or a professional copyeditor, would certainly mark it “wrong”. That is probably why you have heard that it is not “correct”.
The standard if–then forms are the following (notice that would never occurs in the if part):
- If X does this, then Y will do that.
- f X has done this, then Y will do that.
- If X will do this, then Y will do that.
- If X does this, then Y does that.
- If X did this, then Y would do that.
- If X did this, then Y did that.
- If X were to do this, then Y would do that.
If X were certain of this, then Y would do that.
- If X had done this, then Y would have done that.
Number 7 (with were) is given in two forms, because it can be more simply phrased when the verb is just to be. A third form of number 7, employing was instead of were, is sometimes considered uneducated in North America and should probably be avoided in formal writing there.
That gives us 8 (or 9) standard forms, along with 2 that are non-standard, of which your own example is one such that is considered non-standard and perhaps uneducated.
But that doesn’t mean it does not happen.
The answer to the question “What is the correct way to construct a conditional sentence with would?” is then numbers 5, 7 (both flavors), or 8 from the list above, depending somewhat on exactly what you are attempting to convey.
If you are relating reported speech (casual dialogue, especially in dialect), then either of the two non-standard forms might occur. But I would strongly avoid both of those in formal writing.
There actually are a couple of cases cases where would can occur in the if portion in Standard English. For example:
- If only it would snow, we wouldn’t have to go to school.
- If you would please give me some peace and quiet, I will get this finished so we can get out of here.
This is something of a combination of numbers 3 and 7 above. This is close to
- If you would like something, just let me know.
- If you would have something from me, we had best be about it.
. . . where the modal auxiliary is indicating something other than simple time. John Lawler talks about this at some length in this answer. These sort of will and would are allowable, and add more cases to my list above.
The if–only type of if often has a were in it*:
- If only school were closed today, I wouldn’t have to get up.
Which is different from:
- If only school had been closed today, I wouldn’t have had to get up.
The difference is that the second is hypothesizing about something in the past, not the present/future (call it non-past).
In summary, there are a huge whole lot of possible ways of putting together if–then statements in English. Without seeing the original text you’re alluding to, I cannot say whether it would be pass muster as Standard English or not.