The following chart divides all of the appointed Kathisma readings into eight, so that one reads roughly 1/8 of a kathisma at a time, which thus abbreviates them to accommodate parish needs, but also cycles through the reading such that all of the Psalter would be read over time. Only two Psalms are omitted from this chart: Psalms 33 and 50. Psalm 50 is the most commonly read Psalm, and is normally read at Matins elsewhere. Psalm 33 is sung in part at the end of Vespers, and in full at the end of the Liturgy. In parishes in which Psalm 33 is not normally done in full, they might wish to use it under the column of Tone 2.
At a vigil on Saturday evening, one way to do it is to sing the select verses of the first Kathisma (Blessed is Man) at Vespers, as is usual for parish practice, but to do the Psalm from the first Kathisma corresponding to the tone of the week at Matins, and thus one would do three Psalms together at Matins. Click here for a word file, in which these Kathismata are set up to be done this way.
The divisions below for the 2nd and 3rd Kathisma are attributed to St. John (Maximovitch), and are taken from this web page. All the other divisions make no claim to any special authority, and are presented merely as a suggestion.
To see the Schedule of Kathismata during the week, click here.