We omit Mizmor Le'toda from the Pesukeh De'zimra section of the morning prayer service on Shabbat and Yom Tob, including Rosh Hashanah and Yom Kippur. However, we recite Mizmor Le'toda on Ereb Pesach, on Hol Ha'mo'ed Pesach and Hol Ha'mo'ed Sukkot, on Ereb Yom Kippur, on Ereb Tisha B'Ab, and on Tisha B'Ab.
On Shabbat and Yom Tob, immediately after Baruch She'amar, we recite the 92nd chapter of Tehillim – Mizmor Shir Le'yom Ha'Shabbat – and the 93rd chapter – "Hashem Malach Ge'ut Labesh." Some communities have the custom on Yom Tob to omit the introductory verse "Mizmor Shir Le'yom Ha'Shabbat," and to begin with the next verse – "Tob Le'hodot L'Hashem." Others include the introductory verse. Hacham Ovadia Yosef ruled that both practices are valid, and so every community should adhere to its custom.