The advice from AA4PB and W0MT is spot-on. I will just add this:
Before applying for a variance, go to the folks who decide such things and ask how the process works in general terms.
In my case, variances are granted by application to the Zoning Hearing Board (ZHB). Application is made to be on the agenda at a specific public meeting, and cases are heard similar to a court hearing, with exhibits, sworn testimony, etc.
Around here the ZHB does the notification, not the applicant. The applicant can bring witnesses and experts.
In my case (not for a tower, but for an addition) I retained an attorney who had a long history of success with the ZHB. He advised me as to what was a reasonable variance and what wasn't, what information to gather and how to present it, etc. He told me to go to a hearing or two and watch what happens, and I did. At my hearing, he did most of the talking, and the variance was granted.
Yes, it took money and time, but it was a small part of the overall project cost.
73 es GL de Jim, N2EY