By plane, from Delhi is about 1h1/2. Expect delays or cancellation, so allow a buffer day or two between connecting flights, just in case.
You’ll have a 3500m gap between sea level and Leh, so your body will most certainly need to acclimatize. Accute Mountain Sickness (AMS) hits one’s body different from another, starting from minor headaches from which you can get rid of with paracetamol, to nausea and throwing up, and worse to being unable to sustain with it, in which case the only solution is to go back down.
The oxygen being in less big proportion in the air, your breath will come short quickly, especially under effort. Try going to the Oxygen Bar, next to the Tourist Office in Leh, if you feel it will do you good, or just for the experience 😉
By car, the road from Manali takes 2 days (16 hours) by jeep, with a stop in Keylong, through the Rotang La pass. 2500INR per person. Expect delays.
Same by bus, 2 days, but of course, slower and cheaper.
You can also climb up by motorbike, if you’re a warrior and into quite some fun.
The road from Srinagar also takes about 2 days, through the impressive Zoji La pass, with a stop in Kargil, for about 900INR on a jeep. Again, a bus leaves daily, for the most courageous / short on budget.
As said earlier, these roads are only open in summer, and often close for a day or two due to rain and landslides.