A loose kitchen faucet handle may inhibit the flow of water coming from the faucet head. Loose handles may prevent you from shutting off the water as well. Most Moen handles are attached to the faucet using a cartridge. The handle sits over the cartridge head, which can become worn over time with use. A worn cartridge head will loose its shape, causing the handle to wiggle. You may see metal shaving under the handle if this is the case with your Moen faucet.
Turn off the water to the faucet by shutting off the water main leading to the faucet.
Pry off the face of the handle using a screwdriver or remove the handle by inserting an Allen key into the hole at the base and turning it to loosen the handle. Pull the handle up and off.
Inspect the state of the cartridge head. Wrap it with plumber's tape if it is worn and put the handle back on. See if this stops the handle from wiggling. Purchase a replacement cartridge set if this quick fix does not work.
Place the cartridge removal tool that came with the replacement set over the cartridge and turn it left and right using a wrench until it comes loose. Pull the cartridge out.
Insert the new cartridge and reassemble the handle. Test to see if the water turns on properly.