Fortunately there are several avenues to explore. A flying club at your local airport is a great place to start. Flying clubs come in various shapes and sizes, but the general theme is similar: a group that maintains one or more aircraft and spreads the costs of ownership among its members by charging a monthly fee (sometimes an initiation fee as well). There may even be a flight instructor who can train you for the private certificate or instrument rating in the club's airplane at a lower rental rate than you'd pay elsewhere. Depending on the club, membership may mean owning shares in the aircraft, or it may mean that the dues you pay simply buy you access to what the club offers.
Another alternative is to form a partnership ("co-ownership" is the more accurate term) with one or more pilots. As in a flying club, the cost of ownership is spread among members of a (smaller) pool of users, but since you own the airplane, you set the rules and scheduling requirements. On the downside, you have to choose your partners (or vice versa) and live with them.
AOPA Online has lots of information about aircraft ownership options. Start with the Pilot Information Center, which has a section devoted solely to aircraft ownership. Within that section, The Pilot's Guide to Multiple Ownership: Co-Ownership and Flying Clubs gives you an in-depth perspective on clubs and co-ownerships, allowing you to explore the pros and cons of each to determine whether one might be a good fit for your type of flying. You'll also find information on leasebacks to flight schools and fractional ownership programs.
If you have questions about aircraft ownership, talk to a Pilot Information Center specialist at 800/USA-AOPA weekdays from 8:30 a.m. to 6 p.m. Eastern.