The following are only recommendations. Your experience and common sense should prime. If you have any comments to improve these suggestions feel free to drop me a mail.
There are a couple of templates and scripts available for download to ease the NMU process.
Please focus on packages with hi scores.
Roughly the following schedule should be used:
Before you send the intent mail please let everybody know you will be working on that package.
Test the package carefully, build it, install it and use it. Make sure your patch doesn't break anything.
After the upload register to the Package Tracking System. You are responsible for any issue introduced by your upload.
Try to be polite, respectful and patient (even with hostile maintainers). Exchanging insults, privately or publicly, won't help the Debian project at all.
The Debian Developer's Reference has a whole section on NMU. Read it!