The Jaipur transportation system is pretty great actually. The roads and rails are flat and straight so getting from A to B is pretty straight forward.
Jaipur Transportation By Air
Cities like Delhi, Mumbai, Calcutta, Jodhpurs and Jaipur are all well connected to this rather large airport which also has flights to Dubai and a couple of other international destinations. If you leave it until very late you can get extremely cheap tickets from Delhi (about £15).
Jaipur Transportation By Bus
Rajasthan is a very flat state and the roads are all pretty good (relative ot the rest of India). Private buses run from Delhi which takes about 8 hours and should cost no more than 600 rupees. It is also possible to come by Taxi which will cost about 2000 rupees, worth it if you can share with someone.
From Jaipur you can get a 12 hour bus to Udaipur or 6 hours to Bikener and then on to Johdpur. It's up to you but the road system is great so you can go pretty much wherever you want for quite cheap although it's rarely on time.
Indore and parts of Gujarat are also by possible by bus from parts of Jaipur but for you can spend entire days stuck in a bus so it's worth taking the train especially if your short on time.
Jaipur Transportation By Train
The city is a major hub for trains and runs on the broad gauge rails so is connected to all of the big cities of India. Mumbai, Pune (Poona) and Aurangabad in the south all the way up to Jammu in the north. There is a very fancy train that runs from Delhi to Jaipur which I have heard is just an amazing luxury.
There are hourly trains to most other places in Rajasthan like Pushkar, Johdpur and Jaipur etc. Sometimes if you get on the right train during the middle of the day you can travel for hours and it can cost you as little as 20 rupees!!!
Jaipur Transportation, Private car or Taxi
Rajasthan is the perfect place for car sharing. Taxis between cities can be up to twice as fast the buses so it may be worth spending the extra pennies. Ask around your hotel to see who is heading where and you might be able to find some to help split the cost.
Be wary of taxi and rickshaw drivers who “know someone else who is heading that way in car that is leaving soon”. Invariably it is a lie and they just take you to a jewellery shop and leave you there or try some other scams, its a real nuisance, I fell for it twice causing me to miss my bus/train and no cars ever turned up.
Hitch-hiking is a pretty effective way of getting around India and most people in Rajasthan are more than happy to pick up a westerner. Just be careful who you go with, lorries are usually full sweaty men who haven't washed for three weeks so try and avoid these. A Motorcycle is the best way as most other vehicles are packed out with various family members. It's a wonderful feeling cruiseing the desert on the back of a bike with the wind in your hair.