Following are simple measures for saving energy.
Replace devices once they reach the end of their life with more energy efficient devices. Energy efficiency means delivering the same energy service with less energy. An energy service is a useful output of energy, e.g. light, heat for cooking, and sound for speakers. In some cases, you may want to consider replacing devices as soon as possible, as the payback time and net present value is probably much higher (more value or you will spend less in today's money over the life of the device).
Replacing lights with LEDs is probably one example of when it is good to replace devices ASAP. It doesn't matter what kind the light is--CFLs, incandescents, halogens or fluorescent tubes--LEDs are coming down in cost quickly, save much more energy and last for much longer that you will get a payback in energy savings quickly, and then save a lot of money for the rest of the lifetime of the LEDs. If you are not convinced, here is some research that I have done (please excuse the layout in Excel--it is not the best way to present the information).
Turn appliances, equipment and other devices (e.g. lights) off when not in use. Motion sensors for lighting are useful--particularly in commercial, multi-unit residential, municipal, universities, schools and hospital buildings, where there is high traffic, or where people dislike fumbling in the dark to turn lights on. For computers, you can use this program here that turns the monitor off when not in use.
Use power-saving options on your computer, here is some information. You may use an online search engine of your choice to find out more tips. See here, here, here, and here to link a few sources for saving energy with a computer.
Consider changing your routine so that you go to bed early at night and wake up early in the morning so that you save energy on lighting.
Retrofit with insulation in ceilings, floors and walls if you haven't already done so. Putting in insulation in ceilings is fairly straightforward. However, putting insulation in walls or floors is more difficult and may be too prohibitive--which depends on whether you have cavity walls (easier) or not, and the wall material (hard, thick materials are more difficult for insulation than soft, thin materials)
Line-dry clothing instead of using a clothes dryer. On cloudy or rainy days, clothes can be hung on clothes racks on a balcony or inside.
Wear appropriate clothing with temperature—if it's cold then wear enough layers of clothing to keep warm or use a doona, instead of using heating. Also use passive solar design and window treatments and shading measures. Window treatments include having a thick, closely-woven, dark curtain that goes to the floor with a pelmet (a bar on top that stops convective heat loss); using low-e, heat mirror double or triple glazed glass (you could do this if you are building a new house, otherwise for most people you can apply secondary glazing and/or low-e films onto existing windows. Wear light, loose clothing if hot. For cooling, use natural ventilation. If you do these things then you can eliminate the need for mechanical or electrical heating or cooling altogether. However, if for some reason you think you cannot do without a heater or cooler, consider for heating (solar) hydronic heating, heat pumps or high efficiency reverse cycle air conditioners. You can also have open containers of water in front of a fan or window which can be used for evaporative cooling. This method increases the humidity levels in the air so if humidity levels are already high as in tropical or subtropical climates then it is less effective and perhaps more uncomfortable.
If you have a pool, buy a pool cover. Find out more here. If you don't have a pool or spa, consider not buying one and using a beach, natural water body, or public pool or spa instead.
Sealing gaps in doors and windows and using floor snakes can be helpful if you like to keep a place warm (personally I like fresh air and so I leave my windows and doors wide open and just wear warm clothes or wrap a doona/quilt/blanket around myself to keep warm).
Refrigerator: check door seals and repair if damaged. Keep well ventilated. Keep it full with solids or liquids, as the fridge will then not use as much energy to keep it cool.
Installing shading devices on windows is another good way to keep your dwelling cool. Other ways include installing secondary window films, having windows with double or triple glazing and thermal films (to absorb and/or reflect infrared radiation).
If you live in a shared dwelling like an apartment, see if you can make your common property more energy efficient: see here for more