How does one pronounce $a \odot b$?

Usually, when I write such an operator into a problem, I use some variant of an asterisk or star (often a circled asterisk), reading it as "star" in my head. If I'm not using some sort of star, I usually use a circled or boxed X-type symbol and read it as "cross" in my head.

I suggest "sun" for $\odot$ (the standard astronomical symbol).

I try to read from the context what it's supposed to mean. Most of the time I can extract how it's pronounced by just looking at the preceding text.

Without context I read $\odot$ as tropical multiplication and $\star$ as convolution (of some kind), but of course they can represent some other binary operation just as well. For $\cdot$ I could use either dot or times and $*$ could be times or star, I guess.

But most of the time there is a context, isn't it? If not, then my main priority would be to try and find the context.

I would say a⊙b as "a op b"

if is is the only binery operation being defined on the set a and b are from, then I might drop it and write $ab$ and say "a b"

"op" since it is a operator, and odds of there being two operators being used that I don't have words like: star, asterix, cross, mod plus, circ etc, are pretty low.

But if it happened I would be saying "c alt-op d" or perhaps "c op-two d" (though if said fast that is hard to tell from "c op 2d"