The most important consideration when planning a visit to Petra is time.
With 2,640 acres in the Petra Archaeologicl Park itself, there is much to see and with few exceptions you are free to explore everything at your leisure and will. The local people all agree–to properly and fully explore you need five days minimum. While there is certainly enough to occupy yourself for five or more days, two to three days is sufficient to visit all of the highlights in and around the park. One day–or worse yet a morning or afternoon–is likely to bring some disappointment to those who have traveled a great distance. If at all possible, plan for two full days as an absolute minimum.
A day trip to Petra from Amman, is possible either by taxi or bus, but again you are likely to be disappointed and frustrated by having so much to see and do with so little time.
The modern town just outside the ancient city (population about 30,000) is the home for most Jordanian tour agencies. They can arrange for tours of any size and for any reasonable budget. Much of the local population is involved, directly or indirectly, with tourism. While only official, certified guides can be hired inside of ancient Petra (and all other official sights in Jordan), agencies (or you) can hire guides for other purposes such as camping, hiking, backpacking, horse/camel excursions, etc. As always, a reputable agency is the safest and most certain route to plan such adventures far from your home (or country). The people are genuinely friendly and violent crime is nearly non-existent in this HIGHLY family-oriented area.
Plan carefully, plan and pay early, and do not dismiss the idea of a custom, private tour using a Jordanian tour agency. The nature of Jordanian society allows such tours to be reasonably priced and highly fulfilling!
Horse carts, donkeys and camels offer transportation inside the park, but two good legs are the best mode of transport. People with physical disability can certainly visit, but will mainly be confined to the valley floor as most of the higher places are not accessible to those with limited physical abilities. Deep sand in some areas will render mobility devices useless.
The truly adventurous with plenty of time should consider a two- or three-day, mainly valley hike from the Dana nature preserve north of Petra.
The opportunities for photography are spectacular if sometimes challenging. Morning and afternoon light bring out the amazing variety of colors in the stone but also bring deep shadows that will confuse most automatic cameras. Be familiar with the manual use of your equipment!