Getting Index (indices) of selected faces / polygons

One Way

# assuming the object is currently in Edit Mode.
import bpy
import bmesh

obj = bpy.context.edit_object
me = obj.data
bm = bmesh.from_edit_mesh(me)

for f in bm.faces:
    if f.select:
        print(f.index)

# Show the updates in the viewport
# and recalculate n-gon tessellation.
bmesh.update_edit_mesh(me, True)

Another Way

import bpy
import bmesh
from bmesh.types import BMFace

obj = bpy.context.edit_object
me = obj.data
bm = bmesh.from_edit_mesh(me)

for geom in bm.select_history:
    if isinstance(geom, BMFace):
        print(geom.index)

bmesh.update_edit_mesh(me, True)

Further Reading

I encourage you to know what the documentation says. blender.org/api/blender_python_api_current/bmesh.html?