Fossil Collecting/Finding Fossils
Fossils are not to be found in areas of igneous rock (except in some beds between lava flows). In rocks which have undergone metamorphism, they are usually so distorted that they are difficult to recognize or have been destroyed completely. You need to find sedimentary rocks like sandstone, mudstone, shale, and the like.
It also helps to know the age and something of the geologic history of the rock you want to find. Different age rocks preserve different species' fossils. And sediment formed and buried quickly, even if the right kind, may not have very many fossils.
Establishing the age and type of the rocks in your area can be done with the aid of a geological map (usually available from your local state or national geological survey. In the U.S.A., that would be the USGS, United States Geological Survey, web site), or with some geological apps available. These tools will provide you with an idea about the types of fossils to expect, and their age.
Most public libraries should have local geological guide books, but they may be out-of-date. Many hours have often been spent trying to locate a quarry that has since been filled in, or is now in private hands or otherwise inaccessible. College and University libraries are often good sources of information, but may be overlooked by people who are not students. Sometimes the general public can't check out books, but you're free to work in them.
There are a large number of well known fossil collecting localities worldwide. At some of these classic localities fossils have been recovered for a long time. Many such sites are recorded in geological guide books and other sources of literature. At such localities some fossils are almost sure to be found, but generations of fossil collectors will have collected there before, and it's rare to find really good specimens at such places.
A visit to your local museum is often useful. However, one should take into account that many of the inspiring specimens in museum collections may have been collected a long time ago, often when a site was in prime condition. They also usually display the best of the best, and what you see in a museum is not going to be typical of what can be found at any site.
You may also consider joining a rock and mineral club, paleontological, or a natural history society. Up-to-date information from other collectors is usually the best. Often such clubs and societies have access to private collecting sites that would not otherwise be accessible, and field trips are regular events. Supervised parties are usually allowed to collect fossils in quarries and some other locations where individuals are discouraged or not allowed. The staff at operating quarries will often know where the best spots for collecting fossils are.
Another source of fossils are pay-to-dig sites. For a fee, you can dig in an established quarry, including some very good places. Depending on the site, you may get to keep all you find or the owners may rarely reserve a particular type of find (usually some land vertebrates). Know the rules before you pay your fee, and you won't be as disappointed.
Artificial exposures, such as road cuts or quarries, are often good collecting spots. Natural cuts along eroding river banks or coastal exposures are too. Coal mining operations often yield excellent fossil plants, but the best ones are to be found not in the coal itself but in the associated rock deposits called coal measures.
In hilly regions the best sections are often those exposed at the sides of streams that have cut into the bedrock.
Wave washed sea cliffs and foreshore exposures are often good places to search for fossils, but always be aware of the state of the tides in the area. Never take chances by working around cliffs of crumbling rock or clay (many have died attempting it). Wearing a hard hat is a really good idea.
Exposures of softer rocks, such as clays and sands, can be good collecting spots. Inland sections tend to degrade rapidly, becoming overgrown, and are lost.