I am guessing you are cutting from an ILEC to a CLEC (or reverse).
If the CLEC has done thir job, and configured the trunks identically, then the cutover consists of:
1) Porting the old numbers over to the CLEC. This is completely in the hands of the LEC.
2) Unpugging the old trunks and pluging in the new ones.
However in the real world it is quite common that the new trunks won't be identically configured. For example using T1, they may have gotten the line coding or framing wrong. In this case the fastest solution is to change these things int eh PBX, though making them change it is also an option.
Another example involves DID (on analog, T1, or ISDN). If the new carrier gives you more or less digits than the previous then this must be addressed. If you have a complicated dial plan it may be better to have the Telco fix it, but if you have a simple dial plan you may be able to just change it in the PBX.
I guess my favorite description of a cutover is from the "old days" and is from Jane Laino's book "The Telephony Book":
At a typical cutover, a lot of people would be standing around looking worried, smoking cigarettes, drinking coffee and making periodic forays out of the telephone equipment room to reassure the customer:"Yes, at any moment now you will be back in business"
I don't think much has changed in many cases, but I guess they are less likely to be smoking now, and maybe some are drinking lattes rather than coffee
