How to enter private clans where you need to write to be accepted into the clan?

You can do this 2 ways, you can go here: Under "Clans" you will see in small letters, "Recruitment center." You can find the clan's recruitment thread there. If they have one.


Or you can go directly to the clan in the "Clans" tab above, and clicking on "Clans List." For most of the clans, they will have a "Recruitment" tab on their "Clan Page" that you can click on.
Here is an example of [AS]All Stars:
After you click on that, you will be greeted with the thread where you can post your application, but remember to read the information about how to write your application for your best chance to get in. I hope this helps.