Is there a specific aspect of Finance that you are looking to integrate? Everything related to Personal Finance, i.e., understanding your own spending habits, creating financial goals and figuring out how to reach them as well as learning about and investing any savings is a good starting point. You can also make it a point to read the Finance and Economy or Business sections of your local newspapers to start understanding what is going on in the business world :)
Spencer, I started reading the Wall Street Journal daily when I turned 18. I wish I would have started reading about business finance and personal finance years earlier because it would have prepared me on the proper way to use credit cards when I was in college. I didn't use them wisely until 20 years later.
Read and watch anything you can about living a debt-free lifestyle. Then incorporate those principles into your daily life. You may want to go to the library to get help on finding financial material, and check with the library to see if there are free financial community seminars for teens.
I love this question as there can be quite a discussion point around this subject. One way I use finance everyday is to hand write a budget. It's simple math and gives you a good handle on where your personal finances are. There are many great resources out there in the financial world. One that I would recommend would be the "Total Money Makeover" by Dave Ramsey maybe not a read for everyone but I enjoy it and he style is easy and simple to follow and teaches you the basics of personal finance.
I will leave my answer short leaving it open for feedback as there are just so many questions that can be asked on this subject. If you are considering a specific field or line of work, is it college prep, opening your own business.
In 2004, I paid off an apartment I bought for $200k (worth over $2m in 2016).
In 2012, I finally reached my goal of saving $1m.
I came to the US with ZERO dollars and won a scholarship to go to an excellent graduate school.
I am always conscious of how I spend my money on a daily basis. I am a very disciplined consumer and a very goal oriented saver. I continue to save up to this day for the next goal ($2m - $3m in savings). My experience is that if I help my family, I always get back more than what I gave away.
Finance, hmmmm... where to start!? In our country we finance anything from Apple computers to homes. It is very important to understand the basics. The way you can think about finance and your everyday life is establishing good spending habits along with good credit. If you are new to credit work on obtaining a secured credit card to establish credit. Once you receive the card use it responsibly. Keep the usage to under 30% of the credit limit and try to pay your balance off every month. The reason I recommend this is because you will need to finance (borrow a loan) to purchase a car, home, or other items. If you have good credit you will be able to finance loans with a low APR (interest rate). Start while you are young since credit history is an important factor of your credit score (FICO score).