• All classes can read and cast Protection Scrolls (DMG p. 196)
  Protection Scrolls, unless stated otherwise, have a Initiative Modifier of +3 (Sage Advice #152 p. 59)
• Wizards
  • can use (read and cast from) wizard spell scrolls (PHB p. 42 / DMG p. 196)
  • can use spells from scrolls outside their schools (Sage Advice #152 p. 14, Sage Advice #217 p. 84)
  • can use spells from scrolls that are higher level than the wizard's Intelligence normally allows (Sage Advice #219. p. 81)
  • can use spells from scrolls without any restrictions (Sage Advice #219. p. 81)
• Priests
  • can use (read and cast from) priest spell scrolls (PHB p. 48 / DMG p. 196)
  • can use spells from scrolls outside their spheres (Sage Advice #152 p. 14, Sage Advice #217 p. 84)
  • can use spells from scrolls that are higher level than the priest's Wisdom normally allows (Sage Advice #219. p. 81)
  • can use spells from scrolls without any restrictions (Sage Advice #219. p. 81)
• Thieves can use (read and cast from) wizard and priest spell scrolls at 10th level (PHB p. 57)
• Bards can use (read and cast from) wizard and priest spell scrolls at 10th level (PHB p. 61)
• Druids cannot use priest scrolls unless specifically allowed for druids (PHB p. 52)
• Paladins cannot cast spells from clerical or druidical scrolls (PHB p. 39 / DMG p. 196)
• Rangers cannot use priest scrolls (PHB p. 39 / DMG p. 196)

Scroll specific spellcasting information

• Scrolls have a read time equal to the inscribed spell's cast time (PHB p. 125 / DMG p. 196)
• Scrolls are used up and lost if they are disrupted during casting (Sage Advice #157 p. 25)
• Scrolls always has a casting level (for determining level-based variables such as range, damage, duration, and resistance to dispel attempts) of one level higher than the minimum required to cast it, but never less than 6th level. In other words, the act of writing a scroll limits its power (DMG p. 196 + Sage Advice #248 p. 20+22)
• Scrolls are cast at the level at which they were inscribed (DMG p. 196)
• Scrolls require no material components to cast (PHB p. 144 / DMG p. 118)
• No adverse effects associated with casting the spell are suffered by the reader. These requirements or penalties have already been fulfilled or suffered by the creator of the scroll (DMG p. 196)