You could write a letter,if you do,you can write the answers to ever question you should except,still keeping in mind that they will be other questions that your mum will ask that you'll have to answer in person. If you don't live with her,you can call her,that the two simplest ways to tell her. But if you've got the courage,you can tell her in person,it can be really hard to do it this way.
If you are trying the right time to tell her,you need to probably mostly make sure that she is in a good mood,the right time doesn't really exist but it can result is a more dramatic reaction if she is angry or sad.