You say that you work for two lesson companies. You need to know if you are an "employee" (you should have received a W-2 form) or a "contractor" (1099 form). If you're an employee, some taxes have already been taken out. As a contractor, you're responsible for all of it.
I don't know of a specific article for lesson teachers, but here's what I've learned from my accountant over the years:
-mileage - your trip from home to the first school, and from last school home, are NOT deductible. The IRS considers that commuting just like anyone who has a job. Any other trips you take during the day for business are deductible - traveling between schools, going to the music store, etc. Keep records. There are little mileage books you can buy, or various apps you can use. There's a way to deduct actual expenses (gas, insurance, maintenance, etc) but unless you have a separate car for business it's easier to claim mileage on your personal car.
-expenses - anything you use for your business is deductible. Reeds, valve oil, music books, TurboTax. If you pay rent for lesson space that's deductible. It's much cleaner and easier if you keep a separate business account. Deposit your income into that account, pay your expenses out of that account. What's left over is your profit (income) that you can then move into your personal account as your paycheck. Keep your receipts.
-home office - look up the rules, but generally if you have a part of your home that's only for your business, you can deduct a percentage of your house expenses. Calculate the square footage of your home office space. If it's 5% of the square footage of your home, then you can deduct 5% of your electric, water, even things like lawn care. If you also use your home office space for non-work things, officially you can't claim it.
-you can't buy yourself lunch and claim it. The lunch rule seems to change every year, just keep in mind it's more about wining and dining clients or throwing an employee party, not about feeding yourself.
-if you go to TMEA or TBA for business, you can claim that as business travel. Again, keep a separate account. Leave enough cushion in there throughout the year to cover your TMEA costs in February. This CAN include food because you're traveling for business.
-tax savings - when you're an employee, your employer takes taxes out every month and sends them to the government on your behalf. There are also some taxes that your employer pays, when you're self-employed you have to pay them
yourself. Self-employment tax is EXPENSIVE. I set aside 20% of my income into a savings account for taxes. Once you get over a certain level, the IRS expects you to file quarterly tax estimates. Your last quarterly estimate is like doing your taxes as a regular employee, you finalize the numbers and either pay the balance or get a refund.
-accounting - you should learn and use some kind of software to keep track of your stuff. I've been using the same QuickBooks for 15 years now, it works just fine. I'm sure there are other options out there.
Taxes are a much bigger pain when you're self-employed. Good luck!