The direct translation of "Don't + verb" is an order to forbid something and it sounds very strong: 

Don't be afraid. --> 怖がるな。

Don't be ridiculous. --> バカなことをするな。

Generally, we use other form that has the direct translation like "please don't + verb" in our everyday conversation.

Don't be afraid. --> 怖がらないで。

Don't be ridiculous. --> バカなことを言わないで。

I hope this was helpful and my English isn't bad. 

Same as Ryoko-san, 

Very polite way: …しないでください。

 1:Don't be afraid. 
     こわがらないでください。
 2:Don't be ridiculous. 

     おかしなことをしないでください。

In daily conversation, we cut ください

from above sentences.

In addition, in very special casual way, like a mom talking to her childs,

  1: こわがりね〜

  2: おバカね〜

these are not saying "Don't be..." but including those meanings with love.

Please don't say them to someone elder or higher rank people.