The 1st-level Sor/Wiz spell grease [conj] (Player's Handbook 237) has the entry Target or Area: One object or a 10-ft. square, so, for our purposes, an entry of Area: 10-ft. square. The caster picks as the grease spell's point of origin a grid intersection within the grease spell's short range (25 ft. +5 ft./2 levels) and the grease effect is created in each square that touches that point of origin, creating a 10-ft.-by-10-ft. horizontal plane suitable for cooking pancakes or making ogres stumble.
An area spell's caster needs line of effect only to the spell's area's point of origin: "You must have a clear line of effect to the point of origin of any spell you cast, such as the center of a fireball" (176). The caster does not need line of effect to all four squares that are to be affected by the grease spell's area, for example.
An area spell's area can't typically extend beyond the spell's range. The Player's Handbook on Range says, "If any portion of the spell’s area would extend beyond [the spell's] range, that area is wasted" (175). This means, for example, the 3rd-level Sor/Wiz spell fireball [evoc] (PH 231) will typically create a half-circle if the caster picks as the spell's point of origin a point that is at end of the spell's maximum range, and a grease spell will typically only create a 10-ft. wide yet 5-ft. long slick if the picked point of origin is at end of that spell's maximum range.
This DM treats area spells like the grease spell that possess areas of Other ("A spell can have a unique area, as defined in its description" (176)) as bursts unless the spell says to treat them differently, a burst feeling to this DM like the default way effects should behave. Thus, in this DM's campaigns, a grease spell's area won't wrap around a corner like the spread of a fireball spell, but ask your DM.