Tonight in Tefillat Arvit (evening prayer), we make the switch from Barechenu to Barech Aleinu. Barech Aleinu is known as She'elat Geshamim, we're requesting rains, and therefore the key line in Barech Aleinu is V'ten tal u-matar livracha. Hashem should give us precipitation, dew, and rain, in a Beracha (blessing) way, in the right time, in the right amount, etc., etc.
If a person forgot or made a mistake and did not say Barech Aleinu, there are a few important things to keep in mind when correcting. If they remember before they say Baruch Atah Hashem (Blessed are You, Hashem) at the end, simply go back and say from V'ten tal u-matar (And give dew and rain) and say the Beracha properly. Once they say Shem Hashem (Name of Hashem), if they remember at that point, they should complete the Beracha, Mevarech Hashanim (Blesses the years), and, before moving on to Teka Beshofar, just insert V'ten tal u-matar livracha between the Beracha. Since it's something that you repeat for, you can insert it between the Beracha.
If he doesn't remember to insert it between and finds out a little bit later, at Hashiva Shofteinu or Lamalshinim, that he forgot V'ten tal u-matar, don't fret: you can still add it into Shema Koleinu. If you add V'ten tal u-matar livracha, tal u-matar livracha (dew and rain for blessing) into Shema Koleinu, that covers you, and the person doesn't have to go back.
If they miss the correction in Shema Koleinu, then if they remember before the completion of the Amidah (standing prayer), they go back to Barech Aleinu, repeat the Beracha, and continue the Tefillah (prayer) from Barech Aleinu onward in the proper order. If they completed the Amidah and did not say Barech Aleinu V'ten tal u-matar at all, the Amidah must be repeated over again. So it's important for a person to say it from the Siddur (prayer book) and remember to do it. If one is not sure what they did, they kind of zone out. You can assume that for the first 30 days, for the first month, you're habitually trained to say Barechenu and not Barech Aleinu; you can assume that you didn't say it, and you would have to correct for it.