There are vital thinking tools that people well-informed in economics have that most other people do not. These tools are roughly translatable as being the following 8 things. These things are ones that need to be understood, but frequently are not. 1) Almost every action has tangible and intangible benefits, and tangible and intangible costs, and if you haven't considered all of those factors thoroughly you do not understand enough about what you’re doing.
2) Just because there are good intentions and a perceived ethical stance behind a view or an action, this does not mean what you have is a good idea. In fact, quite often good intentions and a perceived ethical stance actually mask the reasons why many ideas are bad ones.
3) Just about everything in life is a trade-off, where something happens at the expense of something else (primarily time, money, and material resources) - and there is rarely anything you can do, or ought to do, that lies outside of this consideration.
4) If there is one thing that should almost never be interfered with it is the mechanism of prices that are dictated by the supply and demand market. Prices are not just sums that tell us the value of something, they are vital information-carrying signals that inform us of the outcome of billions of transactions throughout the world. No politician can know the market clearing price of anything better than the market knows itself.
5) The economic pie is not fixed, nor is it zero sum. If I have a slice of it, this does not mean it leaves less for you, because the economy can keep growing, creating wealth and value for both of us.
6) The principal drivers of human prosperity, increased well-being and economic growth are trade and competition.
7) Just as in the market of goods and services, tax is also something that also ought to be opened up to competitive forces.
(Note on 7: Just as shops and restaurants compete with one another for your custom, so too do governments of nation states in their rates of taxation (they would be able to do this more successfully were it not for the fact that so many people are under the misapprehension that society would be better if the rich were taxed more). Governments are competing with governments of other countries for foreign investment, where attracting more external workers and more capital investment from foreign entrepreneurs benefits the nation. People want to work and invest in nations where they are not taxed too heavily on their income and their investments.
8) To properly understand economics you have to understand incentives. When one person goes out to complete a transaction based on self interest, he (or she) adds a little bit of value not just to his own circumstances, but to every agent involved in the transaction (the seller, the transporter, the manufacturer, those mining for raw materials, and so on). Multiply that one transaction by the billions that have been going on every day in the past century and a half (in particular) and the result is the Smithian invisible hand mechanism that aggregated to all the increased prosperity and well-being the world has seen.
Understanding these 8 points provides the bedrock on which you can build pretty much your entire arsenal of economic understanding, political analysis and societal commentary. Virtually everything you need to speak rationally on any of those three things is bootstrapped by the wisdom of 8 points above.