Pack as tightly as possible. Put your shoes at the back of the case so that they are on the bottom when the case is upright. Fill the corners with little items. Breakable articles should be packed in the middle, between layers of clothing. Some recommend that certain clothes be rolled rather than laid flat. It is surprising how much extra space is left when clothing is rolled tightly. If you pack liquid toiletries in your luggage, they should be in unbreakable, non-eaking containers. However, it is not necessary to take much of these, as they are easily obtained in most places.
Some have found it practical to put a smaller suitcase inside a larger one. This can then be used for bringing home purchases that you make on your trip.