At vespers of the Lord’s day, i.e. on Saturday evening, the entire first kathisma is read (often abbreviated in parish practice). At feasts on other days of the week, only the first stasis, or antiphon, of the first kathisma (“Blessed is the man”) is read. On certain great feasts of the Lord there is no Psalter reading. The same is true whenever a vigil was served the previous night (unless a feast is being celebrated and the rubrics prescribe “Blessed is the man”). There is also no Psalter reading on Sunday evening, with the same exception.
At daily vespers, the appointed kathisma is read, as determined from the appropriate table. As the table shows, the Psalter reading at daily vespers for a good portion of the year is the 18th kathisma, which is the kathisma consisting of the short Psalms of Ascent.
For reading at the Orthodox services, the Psalter is divided into 20 sections called kathismas (“sittings”); each kathisma is further subdivided into three antiphons (also called stases - singular stasis).