Tesco sell something called Carpet Power. It's brilliant. You spray it on by the bucketload, let it soak for a bit, then give it a good scrubb and rinse it clean. Then you stick a folded towel on top to soak up the water.
You can repeat the process if the stain doesn't come right out the first time.
If you throw a whole jug of water over the stain and let it all soak in and then drag a knife blade along so that all the Baileys is in effect squeezed out to one side, then mop it up with kitchen towels by standing on it with all your weight (it takes ages but I have got a whole bottle of red wine out of my carpet using this method and you cannot even see where it was) You might have to do it a few times.