There are 3 borders with Israel to Jordan. The one closest to Jerusalem (Allenby/King Hussein bridge), does require a
Jordanian visa in advanced if coming from Israel, (plus Israeli passport holders are not allowed to use the
Allenby/King Hussein bridge. This border is only opened from early morning till about 1pm, and there are service vans
running all morning between Damascus Gate and the Allenby bridge.
Once on the Jordanian side, one can rent a car and drive to Petra, hire a taxi (make sure to negotiate price and write down the
price on paper (they like to say fifteen jordanian dinar, and then when you get off, they are demanding 50 dinar).
If coming in from Eilat, crossing the border into Jordan, take a taxi to bus station (should cost 7-8 dinar for the 5 minute ride),
where there are service vans to Petra, for about 5 Jordanian. a taxi to Petra should cost around 30-35 dinar.
If you are looking to stay in a cheap hotel in Petra, I would recommend Valentine Inn.
The Petra park, you would have to pay an admissions fee, which is about 21 JD for one day, 26 JD for two days.
You definitely do not need a tour guide, you can cover it by foot, and will be hassled by horse, camel, and donkey
owners offering to give you a ride.
If you come in early, you can take a 4 hour trip up to Har hahor where Aharon hakohein is believed to be buried.
Once inside the park, negotiate a price with the bedoin guide to take you up. (They call it Jabal Aarun).
I have done it on occasions by foot, and by donkey. It's too steep to use a different animal.
Also for more travel info look at
http://wikitravel.org/en/Petra and
http://www.tripadvisor.com forums.
My itinerary that I have done twice:
Take Egged bus to Eilat - from there take a 5 minute taxi to the Arava crossing to Jordan. At the border terminal
the entire procedure should take 15-20 minutes. You have to pay an Israeli departure tax (around 95 shekel, which you can by
by credit card). Once in Petra, a taxi to Petra should be 30 dinar. Or take a taxi to town (7-9 dinar), and from there next to the
Aqaba police station, sort of an outside bus station, service vans go to Petra, in the morning hours for about 5 dinars, and leave
when they fill up.
The Arava border crossing with Eilat is opened from 6:30am to 8:00 pm. After Petra, you can head back South to Aqaba,
and cross back into Eilat, but since it's a humongous circle if you are going back Jerusalem or Tel Aviv - I recommend
going straight up North to King Hussein/Allenby crossing. You can take a taxi, and ask him to take him on the Kings
Highway, instead of the Deserts - which will allow for an extremely scenic route.
In Amman, I stayed at the Palace Hotel
http://www.palacehotel.com.jo/The city of Amman, there is not much to see or due there - you can skip it. There is a service van from Petra to Amman,
but I believe it's only twice a day. In Amman, a taxi to the Israeli border is about 10-12 Jordanian. In the Abdali bus
station, (which I think is by the second circle of Amman) there are shared taxis all morning that go to the border station, leaving
when they fill up for around 3-4 Jordanian. The Allenby terminal is very busy, as it's the only way Palestinians can cross from
Jordan into Jericho, as Palestinians who are not Israeli citizens, are not allowed to use Ben Gurion airport. Once on the Israeli
side, which is near Jericho, there are service vans that drop you off by Damascus gate ( for around 50 shekel). Also,
on the Israeli side, there is a separate line for Palestinians and tourists.
The Eilat/Aqaba crossing is by foot, but Allenby bridge, involves a 5 minute bus ride after going through departure.
In Amman, I stayed at the Palace Hotel
http://www.palacehotel.com.jo/