Geocaching sans GPS
While a GPS receiver is a very useful tool for navigating to the location where a geocache is hidden, it is often possible to do so without a GPS receiver. As long as you can identify ground zero (GZ) within 30 feet or so, you can search for a geocache just as effectively as someone using the GPS system.
Some geocachers use maps and satellite/aerial photos available online. There are links to several online mapping services at the bottom of each cache description page at Geocaching.com. You can use recognizable objects in the map/photo as landmarks in the field, and find ground zero based on its position relative to those landmarks.
Obviously, it's easier in suburban parks where you can tell that GZ is the tree next to the third picnic table (or whatever), but you can also use natural landmarks, bends in the trail, etc. When there is no good landmark at GZ, you can measure distances from good landmarks, and then pace out the distances in the field. Pacing distances from known landmarks often works for offset caches, too.
Other geocachers use classic map and compass techniques that were used for centuries before the GPS system was available.
Another approach is to search likely hiding spots, hoping to find a geocache without even knowing the coordinates. Some have found caches in city parks this way. This technique is also used by those who brute-force puzzle caches. Rather than solve a difficult puzzle to get the coordinates of the cache, they use clues in the cache description, online logs, etc. to figure out likely hiding spots, and then search those spots for a cache.