The splash guard is often part of the main gasket. If the garbage disposer is leaking between the disposer and the mounting flange, inspect the splash guard for damage. If the splash guard is torn or damaged, replace it. On some models, the splash guard and stopper are sold as a unit. If you cannot replace the splash guard separately, replace both the splash guard and stopper.
If the water is leaking from the pipe attached to the garbage disposal, you may just have loose plumbing. There are a couple of ways these pipes are attached. The first and most common way is with bolts. The pipe will have a flange at the end and a metal bracket, which the bolts are insterted into to secure it. A gasket is used between the flange and disposal to prevent leaks. The other way to secure a pipe is with a slip-joint nut and washer. In either case, the the pipe can be loose and leaking. Ensure the bolts and nuts are tight and replace any worn or damaged gaskets or washers.
Highly Likely
06 - Leaking Sink Flange
The sink flange either has a flange gasket or plumber's putty to seal it to the bottom of the sink. If water is leaking through the sink flange, first confirm the flange is tight. If the sink flange is tight and still leaks, you will have to remove it and replace the sink flange gasket, or you will have to remove the old plumber's putty that has likely dried out and replace it with fresh putty.
Less Common
07 - Loose Lock Ring or Mounting Clamp
Most garbage disposals use a lock ring or clamp to attach the disposal to the sink flange. Over time the lock ring or clamp can loosen and cause a leak. Ensure the lock ring or clamp is tight.