First of all you'll need a dual LNB to run two dishes (or a quad if one has Sky+)
The alternative is to fit another dish.
Without any subscription or card you will get VERY limited channels, you won't even get Channel 5, however you can buy a card from Sky (it used to be about £20), which will give you all the Freeview/Free to Air channels, this is a one-off payment.
If you want the same channels that your mum has than you could always run a Co-ax (aerial lead) from the back of her Sky box to your room, if you then bought a Magic Eye (about a tenner) you can control the box from your room.
You will only be able to watch the same channel on both sets if you do it this way, so if she is watching Corrie, so are you, and if you are watching what you want, it's on her TV as well