Before contacting any of the professional identification sources, you should have as much information as possible about your mineral, rock, or fossil: where it was found (road cut, mine or quarry, county, state, level or depth, etc.), when it was found, what others have called it, and so on.
You should first check with members of your club and other clubs in your area, with fellow collectors who collect at the same site, with amateur collectors of note, with your MWF State Director, and in the classic reference books. Midwest Federation committee chairs may be able to suggest other sources in your area. You should call on a professional only after exhausting local resources.
State Geological Surveys will almost all do "eyeball" identification if possible; but because of limited staff time or lack of mineral and rock testing equipment, they should be asked only when all other local sources have failed. Most request that only specimens from their own state be considered. However, some State Geological Surveys are able to do x-ray or spectrographic examination, and (rarely) prepare thin sections for microscopic study. While most will try to identify fossils, they do not attempt to give the genera or species unless preservation of the specimen is excellent. In addition to the services offered by the State Geological Survey, the Geology Department in any university is likely to have equipment to identify an unknown mineral.
Any specimen sent to an outside source should be non-returnable or have sufficient money or postage sent to cover the cost of returning it. Send along a stamped, self-addressed envelope for the results.
Some institutions may charge a fee for this service. Write or call before sending your specimen to be certain they can provide the service desired, and what the fee will be.
Lastly, if all other state sources cannot identify the specimen, the Smithsonian Institution (Washington, DC) may be contacted for help. This is truly a last resort, since the Smithsonian is likely to have a huge backlog of requests and may take months or years to reply.