Sliding Clips with Key Commands

In the Timeline highlight a clip that has room to move on one or both sides. Then, hold down the Option Key and tap Left or Right Arrow. You'll slide your clip left or right by one frame.

Add a Shift as a modifier key so you're holding Shift + Option and tapping the Left and/or Right Arrow keys and it'll slide 10 frames left or right.

The number of frames that it's slid while using Shift as a modifier key is set in User Preferences. To bring up the setting tap Option + Q then click on the Editing tab and adjust the Multi-Frame Trim Size to the number of frames you want.