washing clothes

Hi,

Needed some advice on washing clothes.

I have been doing this for some time now without any chemicals etc, just running the washing machine without it.

However whites are looking quite dirty even when washed!
Not so good when wearing a shirt to work!

How is one supposed to wash clothes and get the looking clean without using evil chemicals?
Clearly I am doing something wrong,

Appreciate any pointers,
Thanks, Hiba.