**JAVA, 100 BYTES (only loop, full code is 156 bytes, see bottom)**

    for(int i=1;i<100;i++){String s=i%3==0?"fizz":"";s=i%5==0?s+"buzz":s;System.out.println(s==""?i:s);}

probably could be a lot smaller, I just started to learn java a few days ago (although I do have experience in other languages), this is the best I can do.
breakdown of how it works, sorry if I get some terms wrong or explain stuff badly

    for(int i=1;i<100;i++) 
just the loop, starts at 1 goes to 100

    {String s=i%3==0?"fizz":"";
Making a string called "s", equal to a value, if "i" is divisible by 3 with a remainder of 0, set "s" equal to "buzz". If it isn't, set it equal to "". 

    s=i%5==0?s+"buzz":s;
set s equal to a value: if i is divisible by 5 with a remainder of 0, set s equal to s + "buzz", if it isn't, set it equal to itself

 

    System.out.println(s==""?i:s);}
System.out.println is just a simple print statement, inside it, check if s is equal to "" (if s wasn't divisible by 3 or 5, it would be "") print i (the number), otherwise print s

feedback is greatly appreciated.
Edit: 100 bytes for just the loop, below is what I think the full script would be, 156 bytes : (

    public class f{public static void main(String args[]){for(int i=1;i<100;i++){String s=i%3==0?"fizz":"";s=i%5==0?s+"buzz":s;System.out.println(s==""?i:s);}}}