Here's a tip. When you download the service pack, don't use the online installer (e.g. Windows Update). Download the full service pack, and save it somewhere accessible (e.g. CD-R or external media, another hard drive or partition... etc) so that you'll always have it to quickly reinstall.

http://www.microsoft.com/ntserver/nts/downloads/recommended/SP6/128bitX86/default.asp

They call it "SP 6a Network Download"

If you install any components from the original Windows NT, you'll want to immediately install the service pack. It really is worth the time, downloading the full deal for NT4 service packs.

Also, if you've got the whole file there's less chance of getting a corrupted install.

As for installing it, just close down all programs and run the .exe. It would be wise to let it back up your current configuration so you can uninstall the service pack if something doesn't work properly afterwards.