Windows. Examine your windows before winter, as they can be the main source of air making its way into your home. Check for drafts and cracks. If you notice anything, speak to your landlord or apartment manager. You can re-seal or shrink-wrap your windows to keep drafts rom coming in. If you like keeping your windows open for fresh air, you still can in the winter but for short periods of time - and definitely do NOT leave them open overnight or when you are out. You don't want to freeze your pipes!
Curtains. A sure way to keep heat inside your apartment during winter months is to close your curtains and blinds, or even invest in thicker curtains to make a big difference in heat retention.
Rugs. If your apartment is not carpeted, rugs will be your best friend through the cold. They keep heat from escaping!
Outlets. Yes, your electrical outlets can produce a draft! A solution is to get a cover for the outlets you don't use, or use expandable foam insulation around the outlet.
Keep the moisture in. Running a humidifier in your apartment during winter will help to beat the dry air.
Doors. Doors also produce a draft and bring in cold air. The main idea is to keep the cold air out, which can be done by putting a blanket in front of the door, buying a draft guard, or making your own.
Radiators. Inspect your radiators and keep them clean at all times. It turns out that dust or dirt sitting on the radiator will absorb some of the heat that is meant for you! If you have a radiator cover, remove it when the heat is on since it can block the warm airflow. It is also important to make sure that drapes and furniture are not covering the radiators.