The leak can be springing from a number of places in your washer. Rule out the easiest fix first.
Check the water supply hoses that attach to the back of your washer. Pull the washer away from the wall and start a wash cycle. As the washer fills, look for leaks along the hoses and at the ends attaching to the washer. If you find any water escaping, the problem is a bad gasket or compromised hose. Those can be replaced by unscrewing them and replacing with new hoses and gaskets. Take your old hoses to the hardware store so you get the right replacement parts.
If the supply hoses are fine but the washer still leaks while filling, then check the internal hoses for any leaks. You may have to unscrew the rear panel to look at the insides of the washer. There are a number of hoses and clamps within the machine that could be the culprit.
If the leaking occurs during the drain cycle, the problem could be the pump. Replacing the pump may require you to tip the washer over to access the pump from below. If you suspect the pump, check out this guide on how to replace it:
[guide|11043|Kenmore 110 Series Washing Machine Water Pump Replacement].
Hope this helps!