The correct way is: "Twenty-four dollars, fifty cents."
We do have colloquial ways of putting this, such as "twenty-four, fifty", but they would not be written this way, only spoken this way.
If there is an actual *coin* in the amount, sometimes people will colloquially use the coin to add on to the dollar. Like this:
$24.05 would sound like "Twenty-four and a nickel."
$24.25 would sound like "Twenty-four and a quarter."
(Oddly enough, I rarely hear this used if there is a dime involved. It's usually just "twenty-four-ten" or "twenty-four dollars, ten cents".)
If there is an amount in cents that is under ten cents, we sometimes will colloquially use the letter "O" in front of it. Like this:
$24.05 will sound like "Twenty-four o-five."
$24.08 will sound like "Twenty-four o-eight"
However, Pouyan's suggestion to use "Twenty-four-five" applies when you are talking about money over one thousand. For example: $24,500 is often heard colloquially as "Twenty-four, five". If you ever visit a car dealership or listen to car advertisements on the radio or TV, it's a shortened way to say the price so it doesn't sound so intimidatingly high. Example: "Check out our brand new Ford starting at twenty-four, five." (Of course we know that it means 24 *thousand* as there wouldn't be any such thing as a car going for $24.05.)
↑ Things change when you get into the millions. $24,500,000 can be spoken as "twenty-four POINT five million". This is slang, and native/fluent speakers understand that it doesn't literally mean 24,000,000.5 -- but the "point-five" or halfway mark of million is "point-five".
I hope this helps! :)