Basic Chinese Pinyin Rules
1. Usage of y and w
When there is no intials before finals starting with i, y shall be added as initial. If there is other vowels after i, i shall be changed to y. For example:

ia - ya

ie -ye

iao -yao

iou -you

ian -yan

iang -yang

iong -yong

 

 

If no vowels after i, just y before i. For example:

i - yi

in -yin

ing -ying

When there is no intials before finals starting with u, w shall be added as initial. If there is other vowels after u, u shall be changed to w. For example:

ua - wa

uo -wo

uai -wai

uei - wei

uan - wan

 uen - wen

uang - wang

ueng - weng

 

If no vowels after u, just w before u. For example:

u - wu

When there is no intials before finals starting with ü, y shall be added as initial no matter if there is vowels after ü. When y added, ü is changed to u. For example:

ü - yu

üe - yue

üan - yuan

ün -yun

 

 

2. Usage of ’ mark
When syllables starting with a, o, e follow other syllables and may make confusions, ’ mark is used to seperate them. For example: 

piao 票

jiang 讲

min ge 民革

xian 先

pi ao 皮袄

ji ang 激昂

ming e 名额

xi an 西安

3. Abbreviations
Abbreviations of iou, uei and uen
When there is initials before iou, uei and uen, they are abbraviated as iu, ui and un. For Example:

niou - niu

guei - gui

luen -lun

If no initials proceed, then they still abide by the rules of usage of y and w shown above.
When initials other than n and l proceed finals ü starting with, ü changes to u. 

nü - nü

lü - lü

jü - ju

qü - qu

 When uo follows initials b, p, m, or f, u is dropped, resulting in bo, po, mo, or fo.

buo - bo

puo - po

muo -mo

fuo - fo

The final er can follow other finals to form retroflection. In the follow case, er is abbraviated as r.
When er is attached as suffix to finals a, o, e u, -ng. For example:  

bar 把儿

mor 沫儿

ger 歌儿

shur 数儿

rangr 瓤儿

 When er is attached as suffix to finals ai, an, en, drop the final letter and er is abbraviated as r. For example:

hair 孩儿

bianr 边儿

pianr 片儿

When er is attached as suffix to finals i and ü, er is shorted as r.

pir 皮儿

qir 旗儿

qur 曲儿

When er is attached as suffix to finals -i, in, and un, the final letter is dropped. 

sher 事儿