First, make sure you have selected the clip you want to split. Then make sure you are on the Video Tools | Edit tab. You should see the button for Split. Next, make sure you have the playback marker somewhere in the *middle* of the clip. If it is at the beginning or end of the clip, it will be grayed out (because it doesn't make sense to split a clip at the beginning; it's already split). Click the button.
Barring all that, you can always use M on the keyboard to make a split in your clip wherever the playback marker is positioned.
So do any of those instructions work?