Summarize this article:

When setting a plumbing fixture in place, excess plumbers putty usually seeps out from the sides. Use any rag or towel you’d like to wipe up this excess putty and discard it. Now that you’re done using the putty, you will want to make sure you leave a clean area behind. Scrub your work area with a soapy sponge to make sure there are no residual traces of the putty. If you notice water seeping out from under your toilet or your drain, you may need new plumber’s putty. If so, take apart your fixture, remove the existing putty thoroughly, and reapply new putty. If new plumber’s putty does not fix the problem, investigate other sources for the leak, such as broken gaskets or seals.

Summary:
Clean away excess putty. Wash area with soap and water. Disassemble parts and apply new putty if you notice leaks.