Keep in mind that not all land forms will be in each arena and some may be added.
Field: You can see the arena two spaces in each direction and see tributes within one space (assuming they are not in woods)
Water: Same as field but helps hp points
Woods: Can not see arena in any direction and only can identify tributes within the same space
River: You can see across the river, if you choose to stay in river it can carry you two spaces in direction of river
Desert- You can see within 3 spaces every direction including the tributes (assuming they are not hidden by woods)
Marsh- You can see 1 space in every direction but only the tributes that are within your space