Be careful. Although you only file your income tax form once a year, depending on your situation, you may have to pay quarterly estimated taxes. If your LLC is profitable to the point where you will be required to pay income taxes and you are not employed by someone else who withholds taxes for you, you will most likely have to pay estimated taxes. Talk to an accountant about this or read IRS Publication 505 Tax Withholding and Estimated Tax.
If you are required to pay quarterly estimated taxes and you don't, you will have to pay hefty fines to the IRS.
The filing of taxes for an LLC can be based on the time when one files an income tax. So you have to file your income tax once already including your LLC.
When you are the only member in an LLC, you are by default what is called a "disregarded entity" which means the IRS treats the LLC as if it doesn't exist for tax purposes. Therefore, you do not even need to file an LLC tax return with the IRS, but instead file it on Schedule C of your personal income tax return.
However, you may have to file a tax form with the State of your incorporation, particularly since many states charge a minimum tax even if your LLC does not do any business.
If you are only an individual, you only need to worry about personal income taxes on April 15th, and state tax deadlines. In addition, if your income is above a certain threshold, you will also need to file estimated taxes, the same way as if you had business income that was personal as well.
Note: This is not legal advice, and does not create an attorney-client relationship.