It's a bit of a Catch-22: if you know exactly how to describe the problem, you know enough that you needn't ask the question!
The resource suggested by IRstuff is for converting between UTM and latitude-longitude -- something i didn't address before, but, i assume is not applicable to you. I assume your "global" coordinates are already in UTM or State Plane or some other planar system. True? If not, ignore the following...
The procedure i describe assumes you're using Copan (see
1. Create a new coordinate file
2. Add or import the global coordinates
3. Assume you'd like one of the global points (call it 1001) to be at local coords 500.0, 500.0
4. Add a new local point (call it 11) at local coords 500.0, 500.0
5. Assume you'd like another of the global points (call it 1002) to be at a local bearing of 00 (ie, local north)
6. Use Cogo to inverse calc a global bearing from 1001 to 1002 (call it bng B)
7. Using Transform by Parameters:
a) Rotate about point 11 by negative bng B
b) Scale by the combined scale factor (if you don't know what that is just keep it at 1.0)
c) Shift from 1001 to 11
d) Transform the points
8. Delete point 11
All original points are now in the local system.
You'd be well advised to contact a local survey engineer/technician for help.