The forest of Lórien was once far larger than it is now, extending south to Fangorn and east across the Anduin to include the region now known as Dol Guldur. The northern borders had no clear definition, but it is almost certain that the forest once extended further north into the Anduin Vales.
By our time period, the Lórien forest has diminished into a wood approximately 45 miles wide north-south and 75 miles wide east-west. It includes both the Naith-- the main part of Lórien, a roughly triangular forest that lies between the rivers Celebrant and Anduin-- as well as a smaller strip of forest south across the Celebrant from the Naith. Caras Galadhon and Cerin Amroth are both in the Naith.
The land from the Celebrant south to Fangorn and the river Limlight is called Parth Celebrant by the Galadhrim and considered to be part of Lórien. Except for the strip of forest across from the Naith, it's an entirely uninhabited grassland. Note that humans use the name "Parth Celebrant" to refer to only the southeastern corner of this field.
Note also that Galadhrim almost never leave the eaves of their forest, not even to go to the grassland south of the woods. No one is allowed to leave the forest unless they are with a patrol led by an Order member ranked Warden or above.
Taken from +EHELP THEME GEOGRAPHY. See also: some IC distances from various locations in Lórien, and the culture travel policy.
Credits for vector-drawn map: here.