Usually it takes about 5 working days to apply for the permits, so the earliest dates you are suggested to entry Tibet are from:

April 5th by train (Use permit scans we send you.)
April 10th by flight (Extra time is needed for mail delivery, because original permits must be checked.)
Due to Tibet's political situation, it is not so easy to travel Tibet. Foreign travelers are required to apply for special permits as well as a China visa.

There are overall four documents that may be required for foreign tourists to travel freely in Tibet.

Chinese visa and passport — You can apply for these in your country.
Tibet Entry Permit — It is a must for foreigners entering Tibet.
Aliens' Travel Permit — It is required to travel to most areas outside Lhasa. You can only obtain it after you arrive in Tibet.
Military Permit — You have to obtain this to travel to military or sensitive areas.
Working with approved Tibet tour operators, China Highlights is able to assist you to obtain all of the above documents if you book a Tibet tour with us.

What are the Typical Tibet Permits?

The main Tibet travel documents are the Tibet Entry Permit or TTB Permit (issued by the Tibet Tourism Bureau) and the Aliens' Travel Permit or PSB Permit (issued by the local police or Public Security Bureau). More details are provided below.

Tibet Entry Permit (TTB Permit)

The Tibet Entry Permit is the key to entering and traveling in Tibet. It is the most important permit and is a must for foreigners entering Tibet. With this permit, you can visit Lhasa, the Potala Palace, Shigatse, and Namtso Lake. Usually a travel agency needs 20 days to apply for this permit. So please send the required documents to your travel agency as early as possible.

Who needs a TTB Permit?

All foreign citizens need a Tibet Entry Permit to enter Tibet.
Hong Kong and Macau residents don’t need a Tibet Entry Permit, but Chinese SAR passports and Home Return Permit (or Mainland Travel Permits) are needed.
Taiwan residents still need to apply for a Tibet Entry Permit. Chinese people living overseas need to apply for the permit if holding a non-Chinese passport.

Aliens' Travel Permit (PSB Permit)

An Aliens' Travel Permit is required to visit restricted areas.

With this permit and Tibet Entry Permit, you can visit Mt. Everest, Nyingchi, and other places listed below. This permit can only be applied for after you enter Tibet, and it requires your original passport.

Places Requiring TTB Permit + PSB Permit

Tsetang: Samye Monastery, Tomb of Tibetan King, Trandruk Temple, Yumbulakhang
Shigatse: Sakya Monastery, Mt. Everest, Rongbuk Monastery
Gyangtse: Pelkor Chode Monastery & Kubum Stupa
Nyingchi Region: Basum-tso, Pomi, Rawo-tso
Places Requiring TTB Permit + PSB Permit + Military Permit

If your itinerary includes some areas in Ngari (listed below), your travel agency will help you to get a Military Permit from the Military Office in Lhasa before you enter Tibet. Then your tour guide can take this certification and TTB Permit to apply for PSB Permit in Tibet.

Nqari Region: Mt. Kailash, Lake Manasarovar, Tsaparang, Ali
These three places are CLOSED to foreign travelers

Chamdo Region: Chamdo, Riwoche, Tengchen
How to Apply for Tibet Travel Documents
To apply for Tibet permits, you have to book a Tibet tour first and hold a valid passport and China visa.

How to Apply for a TTB Permit

A Tibet Entry Permit is available for independent travelers now. You can either travel in a tour group or one man guided tour. To apply for your Tibet Entry Permit, a booked Tibet tour with an approved Tibet tour operator is required (tour itinerary must be shown on the permit). After you book a tour with your travel agency, they will help you arrange it.

Additional Requirements for F visa & Z visa customers: If you are F visa (business visa) or Z visa (working visa) holders, you are required to provide additional information to the Tibet Tourism Bureau to get a Tibet Entry Permit. Your travel agency will send you the requirements after you book the tour, but they are basically as follows:

If you are working in China, these are required: 1) a current Residence Permit (居留许可证, like a visa in your passport), 2) certification in Chinese from your company/school in China (工作证明, using your company’s letter paper, with your name and passport number, and company seal on it).
If you are invited to China for business, research, lecturing; scientific, technological, or culture exchange; short-term advanced studies, or intern practice for a period of no more than six months, certification from your Chinese travel agency is required.

How to Apply for a PSB Permit

Your tour guide will assist you in applying for an Alien Travel Permit. Your tour guide will ask you for your passport and Tibet Entry Permit and submit it to the Foreign Affairs Section of the local PSB with your tour itinerary.

Using Tibet Permits
Only with an Entry Permit can your travel agency help you buy a flight/train ticket to Tibet.

Receiving Your Tibet Permits

Customers whose travel arrangements are made by China Highlights will receive their Tibet Entry Permit from our local office in the city where they depart for Tibet, e.g. in Chengdu if traveling by air. We will send you a scanned copy of your Tibet Entry Permit by e-mail if you enter Tibet from Golmud by the Qinghai-Tibet Railway.

When the Permit Will Be Checked

A scanned copy of your Tibet Entry Permit will be checked at your departure train station.
Your original Tibet Entry Permit will be checked when you check in at your departure airport.
In Tibet the original Tibet Entry Permit could be checked at anytime, but typically when you check in at your hotel and when you enter Lhasa.
You must give the permits to your Tibet tour guide for safety.
Passport and Visa Requirements
Entering Tibet from China

All foreign individuals entering Tibet must hold a passport valid for at least six months. If you are entering Tibet from China, your Chinese visa must be valid. Only travelers with tourist, business, or working visas (not student visas) are permitted.

Enter Tibet from Nepal

Entering Tibet from Nepal, either by the Friendship Highway or by air, requires a separate group visa (a group may be any number of travelers, and may be just one traveler) valid for Tibet from the Chinese embassy in Katmandu. 30–60-day visas are the norm, and it normally takes 2 weeks to obtain it.

Tibet Travel Permit, known as Tibet Visa among westerners, is a special permission from Chinese government and a must-have document for foreign travelers to Tibet. They are required to show it when boarding a train or plane to Tibet.

Note:

To apply for Tibet permits, China visa and passport are required. So Foreigners who enjoy visa-free access to all of China still need to apply for a China visa .

For more please refer to Entering Tibet from Nepal.