Dora Bas Rivka Silver O'H
G-d told Moshe and Aharon that Pharaoh would ask them for a sign. When he did, they were to pull the staff-into-a-snake trick. The brothers went to Pharaoh and did as they had been instructed. Pharaoh responded by calling his magicians. By using sleight of hand, they appeared to replicate the feat of turning staffs into snakes. Aharon "broke the tie" when his staff swallowed those of the Egyptian sorcerers. (Aharon's staff may have actually been in staff form rather than snake form when it did this, which would be even more impressive!)
G-d instructed Moshe to meet Pharaoh the next morning at the river, when he goes to relieve himself. When he does, Moshe should again tell Pharaoh to release the Jews so they might serve G-d. Because Pharaoh refuses, G-d will turn the Nile to blood.
Moses was instructed to have Aharon extend his staff over all the waters of Egypt - all of it would turn to blood! Even water already stored in barrels and jars would become blood. Moshe and Aharon did as G-d instructed; Aharon hit the river with his staff in Pharaoh's presence and the water turned to blood.
Pharaoh's astrologers were able to replicate this feat, as well, so Pharaoh remained unimpressed. The Nile stayed blood for a week.
The obvious question is where the sorcerers got water in order to copy turning it to blood. As we will see with the other plagues, the Jews were unaffected; they had water. Egyptians could acquire water by purchasing it from the Jews (though if they took it by force, it would turn to blood.)
When Pharaoh refused to heed the first plague, G-d sent Moshe back again. This time, when Pharaoh refused to release the Jews, G-d would cover the land of Egypt with a swarm of frogs. Aharon carried this out and, once again, the magicians of Pharaoh's court copied the deed.
Pharaoh summoned Moshe and Aharon and begged them to remove the frogs. If they did, Pharaoh said he would let the Jews go.
"Test me," Moshe said. "You pick the time you want the frogs to go away and G-d will make it happen."
"Okay," said Pharaoh, "tomorrow."
"Fine," Moshe replied. "Tomorrow the frogs will be gone from the land; they'll only remain in the Nile, where they belong."
(The obvious question is why Pharaoh didn't ask to have the frogs removed immediately. Pharaoh figured that Moshe would expect him to say "right now," so he chose another time. This was in case Moshe was merely a clever magician who had "inside information" and was trying to make it look as if he could get G-d to stop the plague on cue. Oh, while we generally accept the Hebrew tzfardea as "frogs," some commentators understand it to mean crocodiles. You have to admit that crocodiles would make for a very different plague than we normally envision!)