Hi, I need to make a cut where the dotted lines are. Can anyone please tell me what the best way to do this might be. Thanks.
http://img52.imageshack.us/f/mouthk.jpg/
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Blender doesn’t have an inset tool so you have to fudge it. Knife tool or select the faces of the inside of the mouth, E (to extrude) / Esc (press the escape key) / S (scale inwards)
It was a bit of work but turned out pretty well I think. Thanks Richard! 
pg
you could also use the knive-exact or knive-midpoints tools. select the faces where you want the cut to be, press K to open the Cut menu and then draw the line where the cut is supposed to be.
You could have also tried deleting the floor of the mouth (the 8 faces squints at picture) and extrude the remaining edges while scaling them to the center by looking at the model from the Top-View (hide the top of the head so you can see through it for this technique). Then you proceed to clean the new mesh by repositioning the faces to make the shape of the lips of the creature and maybe some gums inside to fit the teeth on later 
I may be mistaken, but the (K Key) doesn’t yet work in 2.5 or 2.56 but only in 2.49.
Thanks, This seems like a similar technique to what Richard suggested!
Using K works, but not the same way as in 2.49. You have to hold K and then draw your cut with the LMB. After you finish the cut, you can use the Last Ops panel (or F6) to adjust the cut, making it midpoints or multiple. It’s pretty ugly, but it’s what we have for the time being.
Everyone seems to have there own hat trick. Here is mine. A, select all edges that is in the path of loop. B, subdivide it. C, move the vertices where it needs to be.
Cool method. Thanks for sharing that ridix.
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Thanks this post was helpful, I hope one day blender have a insicion button, that cuts like a breeze…
I believe it already has since this thread is almost 9 years old.
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Anyone? Is this true or we have to wait for the upcoming 2.8 yaaaay!