Footwear is one of your most important things you need to consider in preparation for the Inca Trail. Good footwear will make the whole trek enjoyable, bad footwear will make it memorable for all the wrong reasons.
The Inca Trail is largely made up of a combination of stone pathways and wide dirt tracks. For most of the year the Inca Trail is dry and the ground that you are walking on is firm and solid. Therefore walking conditions are actually very good. In the rainy season from November though until Mid April, the ground can be very different and consideration needs to be taken to accommodate this.
The Inca Trail also has several high altitude passes, and therefore there is a considerable amount climbing and descending along the trail. Your shoes should be supportive, yet at the same time lightweight as lifting your legs in heavy boots will fatigue your body quicker. Although descents may be considered easier than ascents, you are more likely to miss place your footing or slip on a descending path, and therefore you may wish to consider boots that include ankle support.
Open toed walking sandals are not recommended for the Inca Trail, as it is quite common to get a bloody toe when you accidentally kick a large step. Good quality training shoes or sneakers are also okay, providing that the ground is dry.