A couple of things.
LOTR was shot on film finished through a full film colour pipeline and graded via a Digital Intermediate (I am fairly sure) at a place Called The Post House by Peter Doyle in Wellington. If you want more data there is an awesome American Cinematograper article about the whole porcess.
Short answer play with saturation and contrast levels ! ( or spend lots of money and work with film !)
Long answer :
However in terms of replicating a look from the film there are lots of things you can do in your compositng package. You really are talking about a whole host of things here. Its not just a one operation thing. Colour Grading is an artform in and of itself. there are many things you can doto boost colour contast and saturation but they all have differing effects to your overall image.
I think a good place to start is to grab a referance frame of the look you are going for and do a side by side analysis of this with the footage you have,
Looking at things like the overall contast, gamma and saturation levels as well as the colour contrast and induvidial colour levels for red, green and blue.
Once you have done that start by using the atomic (most basic) colour nodes in shake to manipulate your image. I’m taking about contrast/lum , expand/compress, mult and see how far you can get with these. Once you get a feel for these look at the lookup node. Its the business ! I rarely if ever use the colourCorrect tool in shake as I find it far to overstuffed with things i dont need.
The reason I mentioned film pipleines and DI’s at the start is that once you get going with this you will quickly notice how diffierent the image you have (which I assume is 8bit video) is in look and texture to a film frame And also sadly how colour operations are limited when using this particular kind of source material. that said I reckon with bit of hard work you will be getting good results in no time