One common reason a manual transmission does not go into gear after engaging the clutch is because of low hydraulic fluid. When the level is low in the reservoir, air finds its way into the system, so depressing the clutch causes the air to compress without moving the fluid. This does not disengage the clutch plate. Adding fluid to the reservoir and bleeding the hydraulic line usually resolve this problem.
When adding hydraulic fluid, consult the owner's manual. Using the wrong weight or type of fluid prevents the system from working and makes the vehicle difficult to shift, according to HowStuffWorks.
On vehicles that use a linkage rather than a hydraulic system, cables out of adjustment lead to shifting difficulty. The owner's manual or vehicle repair guide provides instructions for adjusting the cables to make it easier to operate the car.
Sometimes, the problem is with the clutch plate itself. Over time, this friction plate begins to wear and needs replacement, making it difficult to get the car into gear. Oil leaks from the engine that drip onto the clutch plate cause the fibers to swell and reduce the clearance of the plate so it does not disengage. Problems with the clutch plate are more serious and usually require the help of an automotive repair shop.