To go to Petra:
Need to reach Jordan 1st :-) By plane or By Car
By Plane about 2:30 hours to Amman
By Car you'll need about 30 Hours drivng through S.A till Amman.
From Amman to Petra:
Best option is to go to The Jet transportation company in Al Abdily, the have daily trips tp Petra, they can manage for you the Hotel and entrance fee as they have several packages and the give the best price ( this is from my experiance )[ any cab in amman will take you there-be careful, they are the best to rip you off, so make sure he starts the meter].
This might be the best time to go as the weather is just right
Have fun in all casse