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The laws for lighting candles on Sukkot are the same as on Shabbat.
This is with the exception of the custom of waving one’s hands over the flames and covering the eyes while the blessing is recited. This is not done as on Shabbat because a flame can be transferred on Sukkot as on the other festivals and there is no need to have lit the candles before reciting the blessing.
The blessing is:
בָּרוּךְ אַתָּה ה׳ אֱלֹהֵֽינוּ מֶֽלֶךְ הָעוֹלָם אֲשֶׁר קִדְּשָֽׁנוּ בְּמִצְוֹתָיו וְצִוָּֽנוּ לְהַדְלִיק נֵר שֶׁל יוֹם טוֹב.
Barukh attah adonai, eloheinu, melekh ha-olam, asher kidd’shanu b’mitzvotav v’tzivvanu l’hadlik neir shel yom tov.
Praised are You, Adonai, our God, Sovereign of the universe, who, sanctifying us with divine commandments, has commanded us to kindle the festival lamp.
If it is Shabbat as well, the blessing concludes:
…לְהַדְלִיק נֵר שֶׁל שַׁבָּת וְשֶׁל יוֹם טוֹב.
…l’hadlik neir shel shabbat v’shel yom tov.
…to kindle the Shabbat and festival lamp.
This is followed by the She-heheyyanu (also written as shehechianu) blessing, which (as mentioned above) is recited on both nights:
בָּרוּךְ אַתָּה ה׳ אֱלֹהֵינוּ מֶלֶךְ הָעוֹלָם שֶׁהֶחֱיָנוּ וְקִיְּמָנוּ וְהִגִּיעָנוּ לַזְמַן הַזֶּה.
Barukh attah adonai, eloheinu, melekh ha-olam, she-heheyyanu, vekiyamanu, vehigiyanu lezman hazeh.
Praised are You, Adonai, our God, Sovereign of the universe, who has given us life, sustained us, and brought us to this occasion.
Adapted with permission from The Observant Life.