Check all available resources for clues. I generally start in this order:
1) Available Family Search profile or sources
2) Any Ancestry profiles or sources
3) Rootsweb profiles and hopefully at least some reference towards sources
4) Geni, My Heritage, or other genealogical research area for help or clues
5) Pure Internet search
And I'm sure there's more (Find A Grave, Billion Graves, Legacy.com, Tributes.com, etc.)
And if all else fails, ask on G2G with specifics - name of person at brick wall, all specific information you've uncovered on them so far, the specific wall you're trying to break, etc. Remember, we will likely follow the same research path you did, so if you tell us what you've done we won't repeat it.
Of course, you could jump to the last option first, if you're already mostly stumped and don't feel any of the suggestions so far would work, which is usually fine.