Right-click on an item to move it from inventory to storage and back, or to drop it. This is much faster then dragging.

Since patch 1.09 you can middle-mouse click instead of a double-click to activate items. Way more reliable than a double-click!

When you hover your mouse over an item in your inventory (tab) and press 1, 2, 3, 4 this assigns a shortcut key. Get used to applying hotkeys. It requires some practice to do this quickly but it is much faster.

Of course you can also change the hotkeys themselves. For example, 2 is for me the most difficult to reach, so I applied Q instead. Imagine you have your Screwdriver on Q, it is very easy to press Q, E, Q to go through a vent. F might be a good choice, too.

If you need to free a hotkey, e.g. before picking up an item that you want to get into that slot, either "apply" a hotkey to an empty slot, or just right-click on that slot at the bottom.