I think you're talking about contractions.
Contractions are shortened versions of words. They help people speak faster because they are not as long as the original words. Often, the original words do not take much time to say, but it is still a significant difference in regular speech. You can use contractions whenever you want to. They are optional, so you do not have to worry about using them, but you should know about them so you can understand others.
See this page for a list of common contractions:
Also, there are informal contractions:
Obviously, you should not use informal contractions in formal situations. They are very casual.
Note that people may use contractions right after any word, not just those on the list. Here is an example:
"That DOG IS destroying my couch!" to "That DOG'S destroying my couch!"
("dog's" is not possessive, so this can confuse people)
"The KID WILL be going to school soon." to "The KID'LL be going to school soon."
Many contractions may very hard to pronounce, but if you listen to their pronunciations, you will understand them.
I hope that helped.