I've just received agreement papers from a publication who I'm freelancing for. There is a section on the bottom that asks for my address, city, social security#, etc, but it also asks where my check is "payable to". What does this mean? Is this my address? If not, where can I find the information needed?
It is your name, or the fictitious name under which you operate. For example, if your freelance front end is called "Zolani the 13th, LLC", then that's the name you want to appear on the check, and not "Mr. John Zolani Doe" that is written in your birth certificate.
They are basically asking for the name of the legal entity that they should write on the check.
You, as a person, are a legal entity, and so you can have them pay you directly, by name. This is in effect a "sole proprietorship" arrangement and it is the situation of most independent contractors; you're working for yourself, and you get all the money, but you also have all the responsibility.
You can also set up a legal alias, or a "Doing Business As" (DBA) name. The only thing that changes versus using your own name is... well... that you aren't using your own name, to be honest. You pay some trivial fee for the paperwork to the county clerk or other office of record, and you're now not only John Doe, you're "Zolani Enterprises", and your business checks can be written out to that name and the bank (who will want a copy of the DBA paperwork to file when you set the name up as a payable entity on the account) will cash them for you.
An LLC, since it was mentioned, is a "Limited Liability Company". It is a legal entity, incorporeal, that is your "avatar" in the business world. It, not you, is the entity that primarily faces anyone else in that world. You become, for legal purposes, an agent of that company, authorized to make decisions on its behalf. You can do all the same things, make all the same money, but if things go pear-shaped, the company is the one liable, not you.
Sounds great, right? Well, there's a downside, and that's taxes and the increased complexity thereof. Depending on the exact structure of the company, the IRS will treat the LLC either as a corporation, a partnership, or as a "disregarded entity". Most one-man LLCs are typically "disregarded", meaning that for tax purposes, all the money the company makes is treated as if it were made by you as a sole proprietor, as in the above cases (and with the associated increased FICA and lack of tax deductions that an "employee" would get). Nothing can be "retained" by the company, because as far as the IRS is concerned it doesn't exist, so whether the money from the profits of the company actually made it into your personal checking account or not, it has to be reported by you on the Schedule C.
You can elect, if you wish, to have the LLC treated as a corporation; this allows the corporation to retain earnings (and thus to "own" liquid assets like cash, as opposed to only fixed assets like land, cars etc). It also allows you to be an "employee" of your own company, and pay yourself a true "salary", with all the applicable tax rules including pre-tax healthcare, employer-paid FICA, etc. However, the downside here is that some money is subject to double taxation; any monies "retained" by the company, or paid out to members as "dividends", is "profit" of the company for which the company is taxed at the corporate rate. Then, the money from that dividend you receive from the company is taxed again at the capital gains rate on your own 1040 return. This also means that you have to file taxes twice; once for the corporation, once for you as the individual.
You can't, of course, have it both ways with an LLC; you can't pay yourself a true "salary" and get the associated tax breaks, then receive leftover profits as a "distribution" and avoid double taxation.
It takes multiple "members" (owners) to have the LLC treated like a partnership, and there are specific types of LLCs set up to handle investments, where some of what I've said above doesn't apply. I won't get into that because the question inferred a single-owner situation, but the tax rules in these additional situations are again different.