1. When a person is deemed to be a Musaafir (traveller according to Islamic Shariah) it is Waajib (obligatory) to shorten the Prayer.

وَإِذَا ضَرَبۡتُمۡ فِى ٱلۡأَرۡضِ فَلَيۡسَ عَلَيۡكُمۡ جُنَاحٌ أَن تَقۡصُرُواْ مِنَ ٱلصَّلَوٰةِ إِنۡ خِفۡتُمۡ أَن يَفۡتِنَكُمُ ٱلَّذِينَ كَفَرُوٓاْ‌ۚ إِنَّ ٱلۡكَـٰفِرِينَ كَانُواْ لَكُمۡ عَدُوًّ۬ا مُّبِينً۬ا (١٠١)

[4:101]When you travel on the earth, there is no sin on you in shortening your Salah, if you fear that the disbelievers would put you in trouble. Surely, the disbelievers are an open enemy for you.

2. A casual reading of the verse indicates that shortening of prayer must be done due to fear, however Rasul-ullah (Sallallahu Alaihi Wasallam) and Sahaba (RA) shortened prayers with or without fear during travel.

و حدثنا ‏ ‏عبد الله بن مسلمة بن قعنب ‏ ‏حدثنا ‏ ‏عيسى بن حفص بن عاصم بن عمر بن الخطاب ‏ ‏عن ‏ ‏أبيه ‏ ‏قال ‏ ‏صحبت ‏ ‏ابن عمر ‏ ‏في طريق ‏ ‏مكة ‏ ‏قال فصلى لنا الظهر ركعتين ثم أقبل وأقبلنا معه حتى جاء ‏ ‏رحله ‏ ‏وجلس وجلسنا معه فحانت منه التفاتة نحو حيث صلى فرأى ناسا قياما فقال ما يصنع هؤلاء قلت ‏ ‏يسبحون ‏ ‏قال لو كنت مسبحا لأتممت صلاتي ‏
‏يا ابن أخي إني ‏ ‏صحبت رسول الله ‏ ‏صلى الله عليه وسلم ‏ ‏في السفر فلم يزد على ركعتين حتى قبضه الله وصحبت ‏ ‏أبا بكر ‏ ‏فلم يزد على ركعتين حتى قبضه الله وصحبت ‏ ‏عمر ‏ ‏فلم يزد على ركعتين حتى قبضه الله ثم صحبت ‏ ‏عثمان ‏ ‏فلم يزد على ركعتين حتى قبضه الله وقد قال الله ‏
‏لقد كان لكم في رسول الله أسوة حسنة ‏

Hafs b. 'Asim (RA) said: I accompanied Ibn 'Umar (RA) on the road to Mecca and he led us in two rak'ahs at the noon prayer, then he  went forward and we too went along with him to a place where he alighted, and he sat and we sat along with him, and he cast a glance to the side where he said prayer and he saw people standing and asked: What are they doing? I said: They are engaged in glorifying Allah, offering Sunnah prayer. He said: If I had done so I would have perfected my prayer; O my nephew! I accompanied the Messenger of Allah (Sallaho Alaihe Wassllam) on a journey, and he made no addition to two rak'ahs, till Allah called him. I accompanied Abu Bakr (RA) and he made no addition to two rak'ahs till Allah caused him to die. I accompanied 'Umar (RA) and he made no addition to two rak'ahs till Allah caused him to die. I accompanied 'Uthman (RA) and he made no addition to two rak'ahs, till Allah caused him to die, and Allah has said:" There is a model pattern for you in the Messenger of Allah" (al-Qur'an, xxxiii. 21). [Muslim]

3. During Travel Salatul Zohar, Asar and Esha are shortened from 4 Rakaat to 2 Rakaat but the rest remain the same.

وعن عائشة، قالت: قد فرضت الصلاة ركعتين ركعتين بمكة، فلما قدم رسول اللّه صلى الله عليه وسلم المدينة، زاد مع كل ركعتين ركعتين، إلا في المغرب؛ فإنها وترُ النهار، وصلاة الفجر؛ لطول قراءتها، وكان إذا سافر، صلي الصلاة الأولى. أي؛ التي فرضت بمكة

Aishah (RA) said: "The salah was made fard in Makkah in sets of two rak'at. When the Prophet (Sallaho Alaihe Wassallam) came to Medinah, two rak'at were added to each salah except the maghrib salah because it is the witr of the daytime, and the dawn prayer due to its lengthy Qur'anic recital. But if one travels, he performs the original prayer [i.e., only two rak'at]. [Ahmed]

4. The majority of scholars in Hanafi, Shaf’ae, Maliki and Hanbali Madhab agree that the minimum required distance for a person to be considered a Musaafir (traveller according to Islamic Shariah) is 4 Burud which is equivalent to 16 Farsakh or 48 (Shariah Miles) or 88 Kilometres or 55 miles.

باب ‏ ‏في كم يقصر الصلاة ‏ ‏وسمى النبي ‏ ‏صلى الله عليه وسلم ‏ ‏يوما وليلة سفرا ‏ ‏وكان ‏ ‏ابن عمر ‏ ‏وابن عباس ‏ ‏رضي الله عنهم ‏ ‏يقصران ويفطران في أربعة برد وهي ستة عشر فرسخا ‏

Chapter concerning when to shorten the prayer; The Messenger of Allah (Sallaho Alaihe Wassallam) used to designate a day and a night journey as travel and Ibn Abbas (RA) and Ibn Umar (RA) used to shorten the prayer and open their fast at a journey of 4 Burd and it was 16 Farsakh. [Bukhari]

5. The intention for travelling the designated distance must be made, otherwise the person would not be deemed a Musafir (traveller) in Islamic Shariah. The intention does not need to be verbally uttered, it is simply done within the heart.

حدثنا ‏ ‏الحميدي عبد الله بن الزبير ‏ ‏قال حدثنا ‏ ‏سفيان ‏ ‏قال حدثنا ‏ ‏يحيى بن سعيد الأنصاري ‏ ‏قال أخبرني ‏ ‏محمد بن إبراهيم التيمي ‏ ‏أنه سمع ‏ ‏علقمة بن وقاص الليثي ‏ ‏يقول سمعت ‏ ‏عمر بن الخطاب ‏ ‏رضي الله عنه ‏ ‏على المنبر ‏
‏قال سمعت رسول الله ‏ ‏صلى الله عليه وسلم ‏ ‏يقول ‏ ‏إنما الأعمال ‏ ‏بالنيات ‏ ‏وإنما لكل امرئ ما نوى فمن كانت هجرته إلى دنيا ‏ ‏يصيبها ‏ ‏أو إلى امرأة ينكحها فهجرته إلى ما هاجر إليه ‏

Narrated 'Umar bin Al-Khattab (RA):  Allah's Apostle (Sallaho Alaihe Wassallam) said, "The reward of deeds depends upon the intention and every person will get the reward according to what he has intended. So whoever emigrated for Allah and His Apostle, then his emigration was for Allah and His Apostle. And whoever emigrated for worldly benefits or for a woman to marry, his emigration was for what he emigrated for." [Bukhari]

6. Shortening of the prayers will commence once the person has left the city limits and cease when the person has re-entered the city limits.

‏ ‏حدثنا ‏ ‏سليمان بن حرب ‏ ‏حدثنا ‏ ‏حماد بن زيد ‏ ‏عن ‏ ‏أيوب ‏ ‏عن ‏ ‏أبي قلابة ‏ ‏عن ‏ ‏أنس ‏ ‏رضي الله عنه ‏ ‏قال ‏
‏صلى النبي ‏ ‏صلى الله عليه وسلم ‏ ‏بالمدينة ‏ ‏الظهر أربعا والعصر ‏ ‏بذي الحليفة ‏ ‏ركعتين وسمعتهم يصرخون بهما جميعا ‏

Narrated Anas (RA): The Prophet (Sallaho Alaihe Wassallam) offered four Rakat of the Zuhr prayer in Medina and two Rakat of the 'Asr prayer in Dhul-Hulaifa and I heard them (the companions of the Prophet) reciting Talbiya together loudly to the extent of shouting. [Bukhari]

Note: Dhul-Hulaifa is outside of Madinah city limits.

7. In addition to Shortening of the prayers a traveller is permitted to delay the obligatory fasts (i.e. of Ramadhan etc) provided that they are made up later.

يَـٰٓأَيُّهَا ٱلَّذِينَ ءَامَنُواْ كُتِبَ عَلَيۡڪُمُ ٱلصِّيَامُ كَمَا كُتِبَ عَلَى ٱلَّذِينَ مِن قَبۡلِڪُمۡ لَعَلَّكُمۡ تَتَّقُونَ (١٨٣) أَيَّامً۬ا مَّعۡدُودَٲتٍ۬‌ۚ فَمَن كَانَ مِنكُم مَّرِيضًا أَوۡ عَلَىٰ سَفَرٍ۬ فَعِدَّةٌ۬ مِّنۡ أَيَّامٍ أُخَرَ‌ۚ وَعَلَى ٱلَّذِينَ يُطِيقُونَهُ ۥ فِدۡيَةٌ۬ طَعَامُ مِسۡكِينٍ۬‌ۖ فَمَن تَطَوَّعَ خَيۡرً۬ا فَهُوَ خَيۡرٌ۬ لَّهُ ۥ‌ۚ وَأَن تَصُومُواْ خَيۡرٌ۬ لَّڪُمۡ‌ۖ إِن كُنتُمۡ تَعۡلَمُونَ

[2:183] O you who believe, the fasts have been enjoined upon you as they were enjoined upon those before you, so that you may be God-fearing,
[2:184] for days few in number. However, should any one of you be sick or on a journey, then (he should fast) a number of other days (equal to the missed ones); and those who have the strength, (still, they do not opt for fasting,) on them there is a fidyah (compensation, that is, the feeding of a poor person. Then whoever does good voluntarily, that is better for him. However, that you fast is better for you, if you only knew.

8. In addition to Shortening of the prayers and delaying of the fasts a traveller is also permitted to perform Mas'ah (wiping) of the socks for 3 days and 3 nights while a resident is only permitted to wipe for 1 day and 1 night.

قال صفوان ابن عسّال _ رضي اللّه عنه _: أمرنا - يعني النبي صلى الله عليه وسلم - أن نمسح على الخفين، إذا نحن أدخلناهما على طهر، ثلاثاً إذا سافرنا، ويوماً وليلة إذا أقمنا، ولا نخلعهما إلا من جنابة

Sayyidina Safwan Ibn Assal (RA) narrates that Rasul-ullah (Sallallahu Alaihi Wasallam) ordered us to perform Masah on our socks for 3 days and 3 nights during travel and for one day and one night when at home when we had put our socks after Taharah and not to take them off for any reason except for Janabah (sexual cohabitation). [Tirmidhi]

9. The person will cease to be  a Musafir (Traveller) when staying at one place for longer then 15 days and should therefore perform complete prayers and fast and perform Mas'ah (wiping) for 1 day and 1 night.

حدثنا ‏ ‏النفيلي ‏ ‏حدثنا ‏ ‏محمد بن سلمة ‏ ‏عن ‏ ‏محمد بن إسحق ‏ ‏عن ‏ ‏الزهري ‏ ‏عن ‏ ‏عبيد الله بن عبد الله ‏ ‏عن ‏ ‏ابن عباس ‏ ‏قال ‏
‏أقام رسول الله ‏ ‏صلى الله عليه وسلم ‏ ‏بمكة ‏ ‏عام الفتح خمس عشرة يقصر الصلاة ‏

Narrated Abdullah ibn Abbas (RA): The Apostle of Allah (peace_be_upon_him) stayed fifteen days in Mecca in the year of Conquest while shortening the prayer. [Abi Dawud]

10. If a person gets stranded at a location (due to a need without having the intention to stay for longer then 15 days) then he may continue to shorten the prayers.