Get heavy duty plastic from the H/W store. The kits are nice, but a pain to get perfrect (no matter what the instructions indicate).
As Yzzim stated, insulate as much as possible.
Figure that with proper insulation you should save about 1/3 of you heating bill.
If some of the itmes are semi-fixed, you may be able to get the owner to compensate you some what for the value increase to the property.
For every exterior wall, put a insulation cover on all outlets (inside and out).
If you can redecorate those walls, hang some type of cloth - creates an air barrier.
Calking is nice for the cracks, however, the air barriers also help.
If you have a screen door, replace it with a storm door.
Make sure that the exterior doors have no air gaps on the frame and also at the floor level.
Treat the basement the same as the living area for the suggestions above for as much as possible.
If you have multiple floors, keep the temp lower in the bedrooms and their doors closed during the day.
Use heavy lined drapes on windows and pull drapes open on the sunny side of the house until daylight goes, then close them to assist in retaining the radiant heat.