Exploring where you live to discover the geology of the area can be an interesting hobby if you are armed with just a little knowledge and have access to a modest library. Take a little time to familiarize yourself with the type of geologic region that you reside in.
Some areas are mostly sedimentary. Others are more metamorphic. Some have been river basins or even seabeds. Knowing a something about this as you strike out will enable you to go beyond just thinking something looks interesting.
Head first for anyplace nearby where buried rock has been exposed. Cutouts for highways are a great place to look. Many times these have carved through many centuries of deposits. Take a few pictures of the layers before you begin. Either have the better of these enlarged or take the time to sketch what you see. This way you can label the different layers.
If you carefully remove some rock samples from each layer and mark it, this will let you be able to identify it on your trip to the library. You may eventually want to invest in your own resource materials after you know what you want to look for. Using the rock and geology books in the library, research the origins and composition of the various rocks. You can note this on your sketch or photo of the site. Date the sketch and samples. If you pick up a cheap file cabinet, you can store these early samples for a while to use as references for future work.
Talk to people who have lived in the area for 40 or 50 years. Have them direct you to strange places like sink holes that you can examine. Go to old river and creek beds and rummage through the rocks that have been uncovered there. Again keep a sketch or photo of the area and label any samples that you may collect.
Over time as you explore more and more areas, you will develop an appreciation for the small variances from place to place. It can become like a jigsaw puzzle as your knowledge increases. In all probability, unless you live next to a major university, after a year or two, you will be the reigning expert on the geology of your home base.