It does depend on your age and no matter how you tell your mom this I'm pretty sure she's gonna be crushed...any good mom would be...you just need to put it all on the table...tell her exactly why you feel it would be better for you with your dad..if it has anything to do with being closer to school or other bros/sisters she might go for it but if it is just cuz you feel she is too strict or you have more freedom at dad's you can pretty much forget it I'm sure..above all, make sure your dad is aware of your plans b4 you even bring it up to your mom..I know, sometimes it sucks to have parents that live apart...good luck.
As ChristyScott said, it would depend on how old you are. It would also depend of course, on what kind of a relationship you have with your mother. If you have a good relationship, you could probably bring it up in general conversation: ask why you are living with her, what the reasons are etc. and perhaps you could ask her then if you could try living with your father for a bit to see what it is like. If you don't have a very good relationship with her, then it'll be easier in one regard - you probably won't be as worried about hurting her feelings - but it'll be harder to convince her. Perhaps speak to your father first and ask him to mention it to her (is this possible?)? Another way would be to write her a letter - if you write to her, you can word what you say very carefully and without fear of 'mucking up' half way through a sentence and saying something unhelpful to your cause.
There's a saying "closed mouths don't get feed" in other words speak up and tell her how you feel. Honesty is the best policy. No reason to live somewhere your not happy. Your happiness should always be first. This is something that you should live by in your future. Don't live the life someone else wants you to live. It's your life live it the way you want. You only have one life here on earth so make the heat of it.
I think u should flat out tell her but do it in a note and sit it on her bed. It will be easier for her to control her emotions than u just telling her in words. It will give her time to think about your decision...
im in the same situation, but im 16 going to college living in london and my dad just moved up north :L i love my mum to bits but i want to get the chance to get closer to my dad. but i am really struggling to find a way to tell mum ? she does an amazing job and i wont forget that but its very hard ?? x