10 Days is sufficient to visit Leh.
Start from Delhi for Manali in the night. You can take a volvo bus. And booked a cab in Manali for going to Leh. Make sure that the cab is a 4x4 wheel, like Xylo or Innova will also manage to make the journey.
In the morning you'll reach Manali. (You can take 1 day break, to prepare youself for The Manali to Leh journey). The Manali to Leh is roughly a 30 hour drive. You can complete it in 2 or 3 days as you feel comfortable.
Between Manali and Leh, you'll definitely have to do a night stay. So Keylong is a good option. You will get decent guesthouses and food.
Right after Keylong there is a place Jispa, where you can do river side camping. But start early from Manali to be able to make it to that place.
Start from Keylong early morning as you need to cover a lot of distance today. By night you should be able to make it to Leh. Booke a hotel, Take rest, as you'll be exhausted. Enjoy the best sleep of your life.
In these two days (third & Fourth), you'll witness the most beautiful landscapes of India. And this is the most difficult part of the journey. You will pass through some of the highest peaks of Himalayas. There will be drastic altitude change. This is what makes people sick (vomiting, acute mountain sickness, low blood pressure etc). Don't worry, read the section on things-to-take at the bottom of this answer.
For this day, I'll recommend, go easy on yourself. Leh is at higher altitude so your body takes time to adjust to it. Oxygen levels are relatively low and hence you'll tire faster. This day you can use to visit the city on foot or hire a bicycle. Roam around in the market. Enjoy Ladakhi food and Yak Cheese. Get yourself some LEH branded tShirts. Talk to people about places to visit. etc etc.
There are nearby places as Pangog Lake, Nubra Valley, Khardungla Pass, and Lamayuru that you can visit one-place per day.You can take bike on rent to visit these places.
Pangong Lake - Remember the scene from the movie 3 Idiots when Kareena Kapoor comes riding on a scooter to meet Aamir Khan? Those of you who have seen the movie, already have seen the scenic beauty of the picturesque Pangong Tso or Pangong Lake.The most notable feature of the lake is the ever changing hues of the lake.The first glimpse of the serene, bright blue waters and rocky lakeshore remains etched in the memory of tourists. There is a narrow ramp-like formation of land running into the lake which is also a favourite with tourists.
Nubra Valley - Nubra Valley Known as Ldumra (the valley of flowers) is situated in the north of Leh. The average altitude of the valley is about 10,000 ft. above the sea level. The main attraction in this area is the Bactarian Camels (Shaggy double hump Camel) around sand dunes, Deskit and Samstanling monasteries.
khardung la pass - Khardung La is a high mountain pass located in the Ladakh region of the Indian state of Jammu and Kashmir. The local pronunciation is "Khardong La" or "Khardzong La," but, as with most names in Ladakh, the romanised spelling varies. There is a cafeteria on the top. You'll enjoy the Maggi there. There is also a souvenir shop which sells T-shirts and mementos branded with "Khardung La Pass" tag, so get one.
Lamayuru - Lamayuru or Yuru Monastery is a Tibetan Buddhist monastery in Kargil district, western Ladakh, India, situated on the Srinagar-Kargil-Leh road 15 kilometres east of the Fotu La at a height of 3,510 metres.There are many monasteries in Leh. Lamayuru is the biggest. If you are religious and believe in spirituality. You'll like talking to the monks there and their life style.
Tenth Day -
Go to Srinagar - Back to Delhi OR Stay in Srinagar ( you can enjoy in houseboat in dal lake in srinagar)
From Srinagar, you can directly take a flight back to Delhi.
Always carry One photo ID card like PAN Card or Driver’s license
you'll have to take doctor prescribed medicine for higher altitudes. They adjust your heartbeat for higher altitude. Doctors can prescribe some harmless medicine.
UV protection Sun Glasses & Sun block cream
Lip balm and Moisturizer / Cold cream
Comfortable trekking shoes or sport shoes
Take proper govt. permits. Two permits are needed, enquire about them
Most Important Thing A Good Quality Camera.