One of the most important of Elizabeth's abilities is to open tears (portals). By opening a tear you can summon various things to the battlefield, starting from maintenance hooks and ending with weapons and Motorized Patriots. Each time you've located several tears close to each other it means you're about to start a fight with a group of opponents or you came across a well-hidden secret. It's wise to analyze the strategic use of each tear before attacking enemy units so that they will be used in the best way.
Another very useful skill Elizabeth possesses is opening locks and safes. This action can be performed only be spending lockpicks and you'll start finding them since chapter eight (only main storyline locks don't require any lockpicks). The best thing about breaking locks is that they give you access to new areas and valuable treasures so make sure to always have a sizeable number of locksmith's tools with you.
Elizabeth has spent her entire life in solitude studying various books. That allows her to decipher Vox code and this activity is always tied to the game's side missions. A reward for deciphering a code is usually the same - receiving access to secret rooms filled with collectibles and other useful items.
During your journey with Elizabeth she will be finding coins for you from time to time. From the gameplay's standpoint it usually occurs in the areas you're exploring yourself trying to find interactive objects. It's also recommend to interact with vending machines often, even if you don't plan to buy anything, because Elizabeth usually examines them to uncover extra money.
Elizabeth's searching skills may also come in handy during combat. Each time you're low on ammunition, health or salt the girl may find a useful item in the area. Elizabeth will be delivering the supplies you ran on low first. For example, if your health bar has been lowered to a dangerously low level before using up almost all ammunition, then you can be sure that Elizabeth will deliver a medical kit to you instead of additional clips. Some time must pass before she can help you again and resume her search for precious supplies.