When enumerating, don’t stick an –ly on the end of the ordinal number. It has become fashionable to do so, but it’s wrong. Use first, second, third, not firstly, secondly, thirdly; there’s no need to add an extra syllable. That goes for last/lastly, too.
Most people wouldn’t even think of saying I contacted the local businesses firstly, typed up the memo secondly, and distributed the plan lastly because it’s obvious that those are wrong. (At least I hope they wouldn’t!) They would say I contacted the local businesses first. (At least I hope they would!) So why say Firstly, I contacted the local businesses?
Ordinal numbers tell the order in which you’re doing something. First is an ordinal number; firstly is not. (I’m sure we all remember learning in school that cardinal numbers are counting numbers—one, two, three, etc.—and ordinal numbers tell in what order—first, second, third, etc.) In fact, despite its presence in some dictionaries, I’m not sure WHAT purpose firstly could serve. It’s grammatically illogical.
Paul’s book–Literally, the Best Language Book Ever and Sherry’s Grammar List