If you get paid for work you do, by another entity, business or person, you could be classified as an independent contractor, and that also means that you are self-employed and may have to pay estimated taxes.
If you choose not to make these payments, or at a minimum put the funds aside to make those payments, then come tax time you may be in for a not so pleasant surprise, and it could be painful.
If you are a newly self-employed earner, you may assume that the appropriate taxes will be withheld as they were when you were an employee, well they aren't, so just be aware that you now are responsible for this administrative task and it can get pretty hairy if you neglect it. Being unaware that taxes aren't being withheld, may mean that you haven't included the tax expense in your budget, so on top of owing those funds you may now have to find those funds if you hadn't put them aside, and you may have to pay a penalty, if you didn't pay them on time.
So be proactive and check your pay stubs now. Are taxes being withheld? If no taxes are being withheld, verify with your client or the entity with which you are doing business, how your income will be reported to the IRS. Make your estimations and start your quarterly payments - which are required on the 15th of April, June, September of the current year and January of the following year.
You can pay your estimated taxes online, by phone or by mail with a check or money order. If you mail your payment in, Form 1040-ES must accompany your payment.
Start saving some funds to make those payments. Don't let it get hairy...