Validation in sharepoint list and column

Validation on sharepoint lists can happen at two levels.

1. On the whole list
1. if validation should happen on the list, please go to "List Settings", and find the "Validation Settings" in "General Settings". Here you can specify an IF statement where all statements that are true will pass the validation, and be submitted to the list.

1. On the column itself
1. please go to "List Settings", and click on the column that needs the validation check. scroll down to the bottom, and add the IF statement. Please note that this method can only validate values against this specific column.

The if statements are pretty much Excel alike:

Examples using "OR":

The OR function accepts two or more Boolean tests that each return True or False. OR returns True if any one of the tests is True.
=OR(YourFieldName="A",YourFieldName="C",YourFieldName="E")
=OR(State="OH", State="IN", State="KY", State="MI")
=OR(Qty=5, Qty=10, Qty=20)

Examples using "AND":

The AND function accepts two or more Boolean tests that each return True or False. AND returns True if all of the tests are True.
=AND(YourFieldName>"A", YourFieldName<"M")     YourFieldName value must be between A and M.
=AND(Qty>5, Qty<100, Qty<>47)      Qty must be between 5 and 100, but not 47.

Examples using "LEN":

As an example, if your part numbers are always 9 characters long:
    =LEN(YourFieldName) = 9
If the part numbers can be 9 or 12 characters long:
    =OR( LEN(YourFieldName) = 9, LEN(YourFieldName) = 12 )

Examples for Pattern Matching

The SEARCH function:  (online help)

• Matches a pattern using "*" and "?". "*" equals zero more characters and "?" equals exactly one character.
• To match an asterisks or question mark character prefix the symbols with "~". 
  Example: "a~?b?c" matches "a?bxc" but not "axbxc". 
• An "*" is assumed to be appended to the end of the match pattern. To limit the length use the AND and LEN functions.
• The comparison is not case sensitive.
• If there is a match, the function returns the position of the match. If the every character is to be matched you would typically test for "=1" or maybe ">0". 
• If there is no match, the function returns ERROR, therefore it must be wrapped inside of an ISERROR function. As we will have a match if there is no error, the ISERROR must be wrapped inside of a NOT function. (online help for ISERROR)

Examples:
Must start with an "a" or "A" and the third character must be a "c" or "C":
   =NOT(ISERROR( SEARCH("A?C",YourFieldName)=1 ))
   Matches: abc   AbC  aXc  a6c aBcDEF
   Does not match:   bbb   abb  ac  a
Match a phone number pattern of xxx-xxx-xxxx: (note: user could type letters or digits or type extra characters.)
   =NOT(ISERROR( SEARCH("???-???-????",YourFieldName)=1 ))
   Matches: 123-123-1234    aaa-aaa-aaaa   123-123-12344444
Match a phone number pattern of xxx-xxx-xxxx and limit the length:
   =AND( NOT(ISERROR(SEARCH("???-???-????",YourFieldName,1))), LEN(YourFieldName)=12 )
   Matches: 123-123-1234
   Does not match: 123-123-12345

Match a phone number and make sure only digits have been used:
The first example here is not a true pattern match. It just extracts the characters we think should be digits and tries to multiply them by any number. If that fails, then one or more of the characters is not a number. (online help for CONCATENATE and MID)
=NOT(ISERROR(1*CONCATENATE(MID(YourFieldName,1,3),MID(YourFieldName,5,3),MID(YourFieldName,9,4))))
   Matches: 123-123-1234    123x123x1234   123-123-1234xxxxx
   Does not match: abc-123-1234
The second example combines the earlier pattern match with a numeric test:
   =AND(NOT(ISERROR(SEARCH("???-???-????",YourFieldName,1))),LEN(YourFieldName)=12, NOT(ISERROR(1*CONCATENATE(MID(YourFieldName,1,3),MID(YourFieldName,5,3),MID(YourFieldName,9,4)))))

The FIND Function:  (online help)
The FIND function is similar to the SEARCH function with two differences;

• FIND is case sensitive.
• FIND does not support wild cards.

Examples Using Dates

You can create rules to limit date ranges by using the TODAY() function or the DATEVALUE() function.
Date must be in the future:
    =YourFieldName>TODAY()
Date must be in the future by "x" days:
    =YourFieldName>TODAY() + 3I.e. If today is the 7th, then valid dates start on the 11th.
Test against a particular date:  (online help for DATEVALUE)
    =YourFieldName>datevalue("1/1/2015")
Date must be between now and the end of the current year:  (online help for YEAR)
    =YourFieldName < DATEVALUE( "12/31/" & YEAR(TODAY()) )This example calculates a DATEVALUE by building a string to represent a future date.
Date must be within the next 30 days:
    =AND(YourFieldName >= TODAY(),YourFieldName <= TODAY()+30)
Date must be a Monday:   (1 = Sunday, 2 = Monday, 3 = Tuesday, …)   (online help for WEEKDAY)
    =WEEKDAY(YourFieldName)=2
Date must be the last day of the month:
=DATE(YEAR(yourDateColumn),MONTH(yourDateColumn),DAY(yourDateColumn))=DATE(YEAR(yourDateColumn),MONTH(yourDateColumn)+1,0)
Date must be the first day of the month:
=DATE(YEAR(yourDateColumn),MONTH(yourDateColumn),DAY(yourDateColumn))=DATE(YEAR(yourDateColumn),MONTH(yourDateColumn),1) 
Note: Some of the more "fun" Excel date functions like WEEKNUM, NETWORKDAYS and EOMONTH are not supported in SharePoint.

Source http://techtrainingnotes.blogspot.com/2015/10/sharepoint-column-validation-examples.html

NOT Function:

If you want to make an reversed IF Statement: =NOT(your formula): e,g: =NOT(AND(Vendor="APMM";UID="Fixed"))