Q:

What decides what's "reasonable"?

In reading a few laws recently, I've seen a lot of non specific words like "reasonably", "expeditiously", and "sufficient".  I'm wondering how judges decide what is "reasonable" when the way the law is written is so subjective .  

A:

Judges do not decide, jurors do (however, if a judge is the fact-finder, then the judge makes such a determination). The main input that the decision-maker gets is a jury instruction. In order to unify "reasonable doubt", "reasonable price", "reasonable delay" and so on, appeal is often made a mythical being, "the reasonable man", so reasonable force would be the degree of force the reasonable man would use in a given situation. I will draw from California criminal instructions ('cuz I have them) but similar instructions can be found across jurisdictions. For example, one instructions says "A natural and probable consequence is one that a reasonable person would know is likely to happen if nothing unusual intervenes". Or from a negligence instruction "A reasonable person would have known that acting in that
way would create such a risk". More detailed appeal to The Reasonable Person is found in the justified homicide instruction:

Defendant’s belief must have been reasonable and (he/she) must have
  acted only because of that belief. The defendant is only entitled to
  use that amount of force that a reasonable person would believe is
  necessary in the same situation. If the defendant used more force than
  was reasonable, the [attempted] killing was not justified.
When deciding whether the defendant’s beliefs were reasonable,
  consider all the circumstances as they were known to and appeared to
  the defendant and consider what a reasonable person in a similar
  situation with similar knowledge would have believed. If the
  defendant’s beliefs were reasonable, the danger does not need to have
  actually existed.
The defendant’s belief that (he/she/ [or] someone else) was threatened
  may be reasonable even if (he/she) relied on information that was not
  true. However, the defendant must actually and reasonably have
  believed that the information was true.

There is no explanation of what it means to be "a reasonable person". Since nobody believes that they themselves are unreasonable, a simple and also wrong way of judging the matter is to subjectively judge whether you yourself would do the same thing, if you were in that situation. 
Very often, instructions do not even bother to say what "reasonable" means, so (re interpreting expert testimony) "You may disregard any opinion that you find unbelievable, unreasonable, or unsupported by the evidence"; (re corpus delicti) "That other evidence may be slight and need only be enough to
support a reasonable inference that a crime was committed"; "Also, before you may rely on circumstantial evidence to find the
defendant guilty, you must be convinced that the only reasonable
conclusion supported by the circumstantial evidence is that the
defendant is guilty", "when considering circumstantial evidence, you must accept only reasonable conclusions and reject any that are unreasonable"
The closest the law has come to articulating an objective characterization of "reasonableness" is in "reasonable doubt" instructions. One characterization is in People v. Feldman, 71 N.E. 2d 433. 

It is not a doubt based upon sympathy or a whim or prejudice or bias
  or a caprice, or a sentimentality, or upon a reluctance of a
  weak-kneed, timid, jellyfish of a juror who is seeking to avoid the
  performance of a disagreeable duty, namely, to convict another human
  being of the commission of a serious crime

A somewhat improved characterization is the Calcrim instruction

Proof beyond a reasonable doubt is proof that leaves you with an
  abiding conviction that the charge is true. The evidence need not
  eliminate all possible doubt because everything in life is open to
  some possible or imaginary doubt

There is room for improvement, but it points in the right direction.
On rare occasions, a law is written that actually includes a definition. The Gas Price Spike Act HR 3784 said

The term ‘reasonable profit’ means the amount determined by the
  Reasonable Profits Board to be a reasonable profit on the sale.

It is then up to the board to subjectively determine what that profit is. (BTW this did not become law). 
[Addendum]
It's actually very difficult to determine what reasoning judges use in those cases where they are the determiners of fact. They will likely call on their knowledge of law, asking "are these circumstances sufficiently like past circumstance A where the defendant was convicted, or more like B where the defendant was acquitted". 

