It isn't surprising that your window air conditioner produces water -- it's supposed to. The water collects on the internal coils, which are cooled by the evaporation of a refrigerant, just like those of a refrigerator. The cooling process dehumidifies the room, which makes it feel more comfortable, and if everything is working right, the condensed water drains outside. When water drains inside, poor installation or cold weather are often to blame.
During normal operation of a window air conditioner, water drips steadily from the condensation coils and collects in a pan on the bottom of the unit. A tube then directs it outside. For the water to flow in the direction it's supposed to, most units must be installed with the outside end slightly lower than the inside one. Check your unit with a torpedo level to ensure it's tilted in the proper direction. If it's level or tilted toward the inside, unplug it and readjust the braces. Or pull the base of the unit toward you and push its top slightly away, until your level indicates a tilt toward the outside. It's best to check for level along the flat bottom on the outside of the unit.
Note: Some units should be installed level because the tilt for drainage is built in. Confirm the proper installation with the owners manual or by looking up the model online.
Besides the main drainage hole that allows water to drip outside, many air conditioners also have a series of small channels to direct water from the front of the unit to the back. Go outside and watch the air conditioner -- if you don't see a steady drip, unplug the unit and clear the drip opening, if present, with a thin wire or similar tool. If water still flows inside, it may be because the internal passageways are blocked. Look for water pooling near the front of the drain pan; if you see any, it's best to get the unit serviced by an HVAC technician.
To work properly, the temperature of the cooling coils must always be above the dew point of the room in which the air conditioner is working. If the temperature drops too low, the coils will ice up, and the melting ice can drip into the room. Several things can cause icing, including dirty filters, dirty or blocked coils, compressor or control problems, or an improper amount of refrigerant in the coils. You can clean the filters, coils and internal mechanisms yourself, but leave servicing the coils, refrigerant or compressor to pros. The coils can also ice up if you run an air conditioner when the outside temperature is too cold. To de-ice a unit in cold weather, turn it off and leave it off, or run it on "fan."
The water dripping inside may not be coming from the coils but from condensation produced as warm air from outside meets the cold air in the room. The warm air condenses on the seal around the body of the machine, and if the seal isn't effective against air leaks, the water can seep around to the bottom of the unit, collect on the window sill and drip onto the floor. To correct this problem, reinforce the seal around the air conditioner with foam or a similar thermal insulating material, or add finger caulk around the vinyl side panels.