I've been paid via 1099 for a decade now, here's a couple highlights/lowlights of the process
1) You need to pay your income taxes quarterly. If at the end of the year you file your taxes and your quarterly estimate pay-ins are off by more than $1000, you can be fined by the IRS. I honestly don't think they're super strict on that, unless you just flat-out aren't paying quarterly at all or something. I've been off by a couple grand(unexpected end of year bonus) before, and have never been fined.
2) You're basically paying double FICO/social security tax, your half and the employers half. This sucks
3) Do your research on what you can, and can't write off as a business expense. If you are writing off car mileage you have to designate how much of your mileage was personal use and how much was business use, you can't just write off 100% of your yearly mileage if that is also your personal car. You also can't write off any commuter miles, if you have to occasionally commute to an office. You can only write off mileage that is used in the service of customers(going to meet a client, delivering a product, etc) Commuting from home to an office is a no-go.
4) You can only write off your home utilities/mortgage as a percentage of your home office space to the whole home. If you have a 2000sq ft home, and your office is a dedicated 100sq ft bedroom, you can write off 5% of your home mortgage/rent/utilities as a business expense.
5) I highly recommend opening a savings account dedicated specifically to your quarterly and yearly taxes. I get my monthly paycheck and immediately put 28% of it into a savings account. Every 3 months I drain that account and send it to the IRS. That money never sits in my personal accounts any longer than it takes to deposit my check and transfer the money. You don't want that money sitting in your main checking account, someone gets ahold of your debit card, commits a bunch of fraud and the bank now has to investigate for a while before you can get your money back, but in the meantime you need to send several thousand dollars to the IRS. Put that tax money in a very safe place, that doesn't have a debit card tied to it at all.
6) If you are going to write off travel expenses, meal expenses, and anything of that sort, keep receipts and notes for everything.
7) If you are going to have to provide your own health insurance benefits, get some quotes on this ASAP. Most people don't realize how expensive health insurance is. Most people that work for a company don't realize that their employer is probably footing 80%-90% of the cost. They assume their $100 a month that comes out of their paycheck is like half. Usually not even close. Just as an example, health insurance for myself and my wife (both in our mid 30s) is about $550 per month, and that's for a middle of the road plan with a pretty high deductible, not anywhere near the best option available(top-tier plans were upwards of $1000 a month for us both)