Usually you will find a plastic gutter on the back wall inside the fridge, often removable for cleaning, leading to a hole or pipe which is the drain.
If the gutter is out of position, or was removed for cleaning and not put back, the melt water may not run into it. If it is not fitted to the hole or pipe, water may not drain away. You will have to look at your instruction book to see how it should be fitted.
Food detritus, especially concealed blood from meat pushed against the back wall, or spilled milk or cream that has turned to cheese, can block the hole or pipe. Often a pipe cleaner will dislodge it.
Having done the inside of the fridge, disconnect it from the power supply by pulling out the plug. Pull it out away from the wall, you will find a plastic dish postioned on top of the motor. This is where the drain water runs, and it is evaporated by the heat from the motor. It will be full of fluff, dust and mould. Clean it out. Do not allow water to drip onto any electrical part. You will see the pipe(s) leading from the fridge and freezer drains. Clean them out with a pipe cleaner or something. You can hoover the dust and cobwebs off the evaporator coils on the back while you have it out.
This is a good opportunity to give the machine a complete defrost, if you have time, especially if it is a frost-free freezer and does not seem cold enough (they have air ducts in the back which sometimes get choked with ice). With luck you will have cleared all blockages and will see clean water dripping out of the pipes into the dish.