! When the "!" symbol is used, that means the statement is NOT true.
if (!flag){ 
  command(s); 
}
Command(s) will be executed only if "flag" is not true. 
Can be used with variables, as in the following example.
if (!myvar==1){ 
  myvar=1; 
}
In this example, if myvar is not equal to 1, then set myvar to 1. (can also be written as: if (myvar!=1))
&& Used as "and".  All statements must be true in order for the commands to be executed.
if (playertouchsme&&playeronhorse){ 
  message Don't touch me with that horse!; 
}
If the player is on a horse AND the player touched the NPC, the text "Don't touch me with that horse!" will be displayed.
|| Is used to signify OR.
if (washit || wasshot){ 
  message Ow!; 
}
In this case, if the NPC was hit or shot, it'll say "Ow!".
== Denotes equals.  Mainly used for variables and strings.
if (myvar==5){ 
  message It's 5.; 
}
So of course this means if myvar is equal to, or "equals", 5, then display the message "It's 5.".
= Is used to assign a value.
if (playertouchsme){ 
  myvar=1; 
}
This assigns myvar to 1 when the NPC is touched.  Do not confuse assigning something, and checking to see if something is equal to something else, it'll mess up your scripts.
+ Is used for addition.
if (myvar==0){ 
  myvar=myvar+1; 
}
In this case, if myvar is equal to 0, then add 1 to myvar.
- Is used for substraction.
if (myvar==5){ 
  myvar=myvar-2; 
}
If myvar is equal to 5, then assign myvar to myvar minus 2 (thus 3).
* Means multiplication.
if (myvar==3){ 
  myvar=myvar*5; 
}
Assigns myvar to myvar times 5 if myvar is equal to 3.
/ Denotes division.
if (myvar=4){ 
  myvar=myvar/2; 
}
Of course if myvar=4, then I need to divide it by 2!
% This is used as a mod; Where a%b = a - int(a/b)*b, this would look like:
if (myvar==8){ 
  myvar2=myvar%5; 
}
Basically it returns the value of the remainder of 'a' divided by 'b'.  So myvar2 would be 3, since the remainder of 8 divided by 5 is 3.
^ Powers, or Exponents;  ^0.5 = squareroot
if (myvar==9){ 
  myvar ^.5; 
}
This would take the square root of myvar.
a += b Shorthand way to add.
if (myvar==0){ 
  myvar+=3; 
}
Is the same as:
if (myvar==0){ 
  myvar=myvar+3; 
}
Just a shorter way of doing things =)
a -= b Same as above but for subtracting.
a *= b Same as above but for multiplication.
a /= b Same as above but for division.
a ++ For the really lazy.
if (myvar==0){ 
  myvar++; 
}
Which is the same as:
if (myvar==0){ 
  myvar=myvar+1; 
}
The difference in this shorthand method as opposed to the other is, "++" is like adding 1 to the variable.  The other method "+=number" allows you to add any amount.
a -- Same as above, but for subtraction.
min(a,b) Calculates the min of a,b
max(a,b) Calculates the max of a,b
a in b Used to check if the specified value is in the specified array.
myvar=3; 
myarray = {1,2,3,4,5}; 
if (myvar
in
myarray){ 
  message Yes.; 
}else{ 
  message No.; 
}
This checks to see if the value of 'myvar' is also the value of one of the indexes of 'myarray'.  Note that you can also do: 
myvar
in |1,5|  to see if 'myvar' is greater than or equal to 1 and less than or equal to 5 
or 
myvar
in
<1,5>  to see if 'myvar' is greater than 1 and less than or equal to 5.
random( a, b ) Assigns a random number to a variable.  Such as: myvar=random(1,5) This will set "myvar" to a random number between 1 and 5.  It will not be a whole number.
sin( a ) The sine of an angle.  This is in radians, NOT degrees, to convert from radians to degrees multiply by (180/3.14).
cos( a ) The cosine of an angle in radians.
arctan( a ) The arctan of an angle in radians.
int( a ) Rounds off the variable to the nearest whole number.
abs( a ) Finds the absolute value of a variable. |a|
log(base,x) what exponent the base must be powered to in order to reach x log(2,8) = 3 because 2^3= 8