When do we say Tachanun
Tachanun is said on ordinary weekdays at Shacharit and Mincha, and omitted on Shabbat, festivals and special days. In the siddur it appears as a section inside the prayer. On days without Tachanun the section is not said, according to the calendar. In Shacharit it comes after the Amidah, and in Mincha in its place in the nusach. In the digital siddur you can open Shacharit or Mincha and see the section for the day.
Is there Tachanun on Shabbat?
No. On Shabbat and many festivals it is omitted.