One who mistakenly invokes rain in the summer must go back and correct her mistake, since there is no praise in mentioning rain at that time. If she did not yet finish the berakha, she goes back to the beginning of it and says “Morid ha-tal,” as should be recited in the summer. If she already finished the berakha, she must start the Amida over from the beginning in order to recite it properly (SA 114:4).
One who mistakenly did not invoke rain in the winter but instead invoked dew as though it was summer need not repeat it since she invoked praise that relates to water. However, if she did not mention dew either, she must repeat the Amida, since she omitted such important words of praise (ibid. 5).
One who mistakenly requests rain in the summer: since she made an inappropriate request in Birkat Ha-shanim, she must go back and correct it. Therefore, if she did not finish her Amida yet, she returns to Birkat Ha-shanim, recites it properly, and continues in order from there until the end of the Amida. If she already finished the Amida, she repeats the Amida properly from the beginning (ibid. 117:3).
If, by mistake, one did not request rain in the winter, it depends how much of the Amida she already recited. If she did not yet reach Shome’a Tefila, she continues her prayer and when she arrives at Shome’a Tefila, in which one may make any request, she requests rain, thereby correcting her mistake. However, if she already passed Shome’a Tefila, she must return to Birkat Ha-shanim, recite it in accordance with the halakha, and then continue in the proper order, repeating all of the berakhot that come after Birkat Ha-shanim. If she already finished the Amida and was about to take three steps back, her prayer is considered lacking since she did not request rain, and it must be repeated properly in its entirety (ibid. 4-5).