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I'm used to seeing summation capital sigmas with a "start" at bottom and a "stop" at top and would say the sum from i to 100 or whatever. But in this case, there is just a y at bottom.

How would I write this out so a screen reader would be able to read it aloud and get the correct idea across to the listener?

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    I would interpret this as the sum of all values of $f(x,y)$ over all possible values of $y$ given a fixed $x$. It is rather uncommon to see *just a letter*. It is better to specify what range of values or set of values $y$ can take, and would be better written in my opinion as $\sum\limits_{y\in Y} f(x,y)$ where $y$ ranges over all values present in the set $Y$. – 2017-01-04
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    Just out of curiosity, are you working on a screen reader? Second question I've seen =) – 2017-01-04
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    @ZirconCode Yes, unfortunately I am writing screen reader text and there are a number of symbols I'm unfamiliar with how to say. – 2017-01-04

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I would say "sum of $f$ of $x$ and $y$ over all $y$." This is usually what is meant when no upper or lower limits are given.

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It is an abbreviation of summing over a set, which is usually clear from the context. Example: In Linear Integer Programming we could have some set $V$ representing $n$ nodes and some value $c_i$ for each node $i \in V$. The following terms are equivalent $$\sum_{i \in V}c_i \quad \text{and} \quad \sum_i c_i.$$ The advantage is that is saves time but on the other hand it is lacks formallity.

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It depends on context. Sometimes it means "sum over all possible values of $y$" (where which values of $y$ are allowed should be clear from the context), but sometimes it means an indefinite sum or "anti-difference", analogous to an indefinite integral or antiderivative:

$$ \sum_y f(x,y) = g(x,y)\ \text{where}\ g(x,y+1) - g(x,y) = f(x,y) $$