How is the CPU secured to the socket on the motherboard?

It depends on the type of processor being installed.

Most older processors and processors from AMD employ a socket installation mechanism called Zero Insertion Force (ZIF) in which an arm operates an internal clamping mechanism on the pins. When the arm is lifted, the pin clamps are loosened, allowing the processor to be inserted and removed easily. Once a processor is installed, the arm is lowered and secured, causing the pin clamps to secure the pins (and thus the processor) in place.

Newer processors from Intel (Prescott P4s, the Core 2 line, and later) don't have pins--the pins are actually in the socket; thus why they're called Land Grid Array setups. In these cases, the contact force is provided by a special cover (called a load plate) built into the socket. Once the processor is properly placed, the load plate flips on top of the processor and then secured by an arm.

In both scenarios, further securing force is provided by the cooling system (usually a heatsink and fan) that is placed on top of the processor. Socket designs specify how the cooling systems are to be secured to the motherboard. Their installation further secures the processor into the socket.