NEO FFI Scoring
The test manual describes how to calculate raw scores for the NEO-FFI. If you have been asked to do an analysis of the NEO-FFI then you should be given access to relevant details in the test manual. If you don't have access, you may wish to contact your local psychology department. They will often have a test library with the NEO-FFI manual. Alternatively, you can contact a test distributor, although there are often educational requirements in order to be allowed to purchase such a manual.
This website seems to provide a web description of how to obtain raw scores for the NEO FFI. For norm referenced scores such as t-scores, presumably you would need access to norm tables supplied in the test manual. One exception would be where you are using your own sample norms as the distribution. In this case of t-scores, you would convert raw scores to z-scores and then multiply by 10 and then add 50. See for example this article on standard scores.
General scoring advice
In general, when scoring psychological tests, the most common approach is to use a unit weighted sum or mean of items after item reversal. I have a post that describes this in more detail with reference to SPSS and R. So, you simply need to know which items belong to which scales and which items need reversing.