Firstly, you will need to determine whether you will require alternative lighting for the duration of the clean (as you won't be able to turn the chandelier on whilst you are cleaning it). You will also need to ensure that the chandelier has been switched off (place a piece of tape over the button to prevent someone from accidentally turning the chandelier on whilst you are cleaning it) and that the globes are cool.
Next, cover the light bulbs so that you do not damage them whilst cleaning the chandelier. You can do this in a number of ways:
You will also need to place a drop cloth or tarp underneath the chandelier to prevent your floor from becoming dirty or grime-covered.
Buy a special crystal chandelier cleaner from a lighting retailer, or mix your own solution together - one part isopropyl alcohol or ammonia added to three parts water is sufficient. Put this solution into a spray bottle. Spray every part of your chandelier with the solution, but try to avoid wiring and other electrical components (as water can cause them to short circuit).
Leave your chandelier to drip dry (this is where the drop cloth comes in handy!), which may take a few hours. If you feel that your chandelier is too dirty for this cleaning method (meaning that the dust will just be left streaky instead of completely removed), you can wash each individual crystal with the isopropyl alcohol and water solution.
Once your chandelier has completely dried, you can remove the sandwich bags or socks or whatever you have used to protect the globes. If your globes are looking a little dusty themselves, you can dip a soft cloth into the isopropyl alcohol solution and give them a quick wipe. You will then need to let these components completely dry (it is best to leave it overnight) before turning the chandelier on again.