Rogation days are traditionally days of prayer (particularly in the form of a procession accompanied by a sung litany of the saints), and fasting.
The three 'minor' rogation days before Ascension date back to the fifth century, instituted originally by Bishop Mammertus of Vienne (c470). The practice quickly spread throughout Gaul - the Council of Orleans in 510 ordered their use for example. Rogation days were not adopted in Rome, though, until the early ninth century.
Their key purpose is to appease God's anger at man's transgressions, to ask protection in calamities, and to obtain a good and bountiful harvest.
You can find the litany and prayers in the Diurnal at pg (200) and the full chants in the Processionale Monasticum. If said privately, it is usually done after Lauds.
In earlier versions of the Office, there were readings at Matins and a collect specific to the rogation day. In the 1962 monastic version these have, unfortunately, been stripped out of the Office, but I have put up the readings over at the lectio divina notes blog, and here is the collect in case you want to use them devotionally.
Praesta quaesumus omnipotens Deus: ut qui in afflictione nostra de tua pietate confidimus; contra adversa omnia tua semper protectione muniamur.
Per Dóminum nostrum Jesum Christum, Fílium tuum: qui tecum vivit et regnat in unitáte Spíritus Sancti Deus, per ómnia sǽcula sæculórum.
24Let us pray.
Grant, we beseech thee, O Almighty God, that we who in our tribulation are yet of good cheer because of thy loving-kindness, may find thee mighty to save from all dangers.
Through Jesus Christ, thy Son our Lord, Who liveth and reigneth with thee, in the unity of the Holy Ghost, ever one God, world without end.