TurboTax will estimate taxes and print the quarterly vouchers for you when you do your return, but you will have to send the payment to the IRS yourself. If you don't have 1040-ES vouchers at present, you can go to the IRS website and download and print them (see link at bottom).
The Small Business Administration has some pointers on how to do and pay your estimated taxes. You might look at this.
Generally, the thing you need to remember is that you, as a self-employed individual (your side job) are responsible for paying your self-employment taxes, which are the Social Security and Medicare taxes that your employer pays half of and which are sort of invisible to most employees because they are removed from wages before you ever see them. The self-employment taxes are 15.3% of your net self-employment (SE) income (reported on Schedule C).
So, think about your tax return as if you only were an employee. What tax bracket would you be in? 10% 15% (yes, the brackets are changing for 2018). If you determine that as an employee, your tax bracket is 15%, then for every dollar of additional income, you would owe $0.15 in federal income tax.
Now, as a self-employed person, you have to add the 15.3% SE taxes to that, for a total of 30.3% in taxes for each dollar you earn as a self-employed person.
Now you start to see why consultants and contractors charge so much - they have to cover the SE taxes and any benefits like health insurance, life insurance, retirement, etc. that they don't have as an employee. Fortunately, since you are still an employee, it's only the SE taxes you have to worry about, not the other benefits.
To offset this 30.3% tax, you have the advantage of being able to deduct business expenses on Schedule C. It is much easier to deduct things on Schedule C than deducting employee business expenses on the 2016 or Schedule A. And the more you are able to claim business deductions, the more your Schedule C net income is reduced, which reduces your federal income tax and the SE tax.
So what I would do (and actually did for years) is to arrive at some percentage of my gross that I wanted to set aside in an account, and then I would pay it quarterly. If you base it on what you earn in a quarter, then this will take care of the normal ups and downs of your self-employed income.
For example, you might look at your normal expenses and determine that 25% is a good percentage to set aside.
In this case, you would set aside 25% of your monthly billing as a contractor, and then each quarter, pay what you have set aside using your form 1040-ES. If your business expenses are reasonably predictable, this method should keep you in the ballpark without having to do the intense calculations that the IRS suggests that you do in the Instructions for the 1040-ES.
