They show how he got back in the episode when he returns to Earth which the episode is called Mystery Revealed.
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Goku returned from defeating Frieza in episode 121 of season four after Trunks chopped Frieza into pieces and blasted him along with his father King Cold
Frieza does not get killed by Goku. Future Trunks is the one to kill Frieza.
Goku survived after beating Frieza by taking Captain Ginyu's ship, which had survived the destruction of Namek. He landed in the planet of the Yardrats, and stayed there until returning to Earth.
Yes, Goku wins the battle and leaves in time but the people on earth try to wish him back to earth but he decides to train in space as a super sayan than come home with his family. But, Frieza is still alive and with his dad king Cooler to give revenge to son Goku but Goku is still not on earth yet and might come home to the horror on his friends death.
Frieza 100% it is obviously shown when Frieza killed Goku. I forget which episode but when Frieza 100% was fighting ssj Goku and he killed him by drilling him into the lava and then sending energy blasts down the hole. Coincidentally, the wish to restore everyone killed by Frieza and his men, restoring Goku. Not only that but because of the saiyan's natural zenkai he got a boost in power. This allowed him to defeat Frieza since he had been damaged by ssj Goku's attacks and because of the power loss due to using 100% power.