There are daily flights from Delhi to Leh, these flights are operated by Indian Airlines, Jet Airways and Go Air. You can check availability, fares and do online booking for flights by logging onto:
Another option is coming by road either from Srinagar or from Manali. Both of these routes take two days with one night stop on the way. These roads are mostly open from May to October.
In that case the best option is to fly from Delhi to Srinagar, and take a jeep ride to Leh which takes only 10-12 hrs. For example if the fare to Leh is approximately 15000 INR to Srinagar it should be around 5000INR. The cost difference is not due to distance its just because from Srinagar they have almost 30 flight a day, and to Leh they have only 4-5 flights a day. While driving to Leh from Srinagar you can cover most significant and must see places in Ladakh. First famous destination is Sonamarg of course that is in Kashmir, than Zojila Pass, Drass, Kargil, Mulbek, Lamayuru, Rizong, Alchi, Likir, Basgo, Phyang and Spituk. Even you can take another route to Suru valley and Zanskar from Kargil.
Abruptly going to a height of 3500 m, one naturally feels a difference. Your body reacts and behaves differently in rarified air at high altitude. What you need to do is just take it easy and give some time to your body to adjust in to less oxygen (hypoxia) by a slow physiological process called Acclimatization. Time taken for acclimatization varies from person to person; usually you nee atleast 2-3 days in order get well acclimatized and you need to take complete rest for the 1st day even if you are feeling fine. Drink plenty of fluids at least 3-4 litres. Diet should be high in carbohydrates, less oily and predominantly vegetarian. Avoid excess of alcohol and tobacco in any form.