There are many other ways to say the same thing, and those other ways can be so much more descriptive and give the story depth. There are simple replacements: replied, answered, stated, remarked. These say the same thing but stop the redundancy. It doesn't feel as much like a Dick and Jane book.
Some authors suggest avoiding dialogue tags altogether which would eliminate the too much ‘said’ problem. I think not having them with every piece of dialogue could be a good thing, but tossing them completely out I think is a really bad thing. These tags can be very beneficial when you find other words to use instead of ‘said’.
“The train will be here before he gets the job done,” Jack said.
Depending on the rest of the writing before and after this sentence, we probably know who said it. Dialogue tags work better if there would be confusion as to who said what. Let’s assume in this example we need it, but we’ve used ‘said’ enough as it is. We don’t want our readers to think we have a limited vocabulary.
What is Jack’s emotional state? If he is excited, you could say ‘Jack exclaimed’. Other words for this emotion would be shouted, pointed out, insisted. Is he angry? Then use barked, spat, snarled.
Notice how the replacement words become something like adverbs in describing the action instead of stating the action. We know Jack said the words. The quotation marks told us that, but how did he say them. Give us an idea of his emotion so we can hear the words. ‘Said’ is bland. ‘Snarled’ gives the words a whole new meaning.
When you are editing your own work, focus on how many times you use ‘said’. Go through and replace every other one with a different word that better fits the emotion and mood of the dialogue and speaker. That one ‘small’ change can give depth to your story.