Well, you're wrong. One of the best things about freelance writing is you don't have to spend a lot of money up front to begin writing and hopefully making some money from your work.
You will need some basics though:
Paper of some kind (you can frequently get this free), ask around, companies change letterhead and throw out the old, some notebooks get partially used before someone tosses it out - tear out used pages & use the rest. Use the back side of one-sided paper someone has thrown out. Be creative and think. Watch for sales at office supply at the beginning of the school year; they frequently offer notebooks at $.01 each or maybe $.05 each.
Writing implement - you can score free pens in the bank or maybe left lying around somewhere. You can get them really cheap at beginning of school year sales. They're probably just lying around the house and lots of places hand them out as promos.
A flash drive whether you actually own a computer yourself or not. Again, watch for sales at office supply stores. I've gotten a 3 meg flash drive for as little as $5.00 - sometimes with rebates you can get them free. Maybe a friend has a bunch lying around and wouldn't mind sharnig one with you. Ask for one for a birthday or holiday gift.
Okay, so you have the rudimentary basics. Here are some things you can get for free or use for free. Some of this may not be terribly convenient, but convenience usually costs $$$ so once in a while that has to be sacrificed until you can afford your own set-up.
1. First resource: Public Library - Yes, they have computers for public use. Most want you to reserve time so keep that in mind. If using this resource it's best if you do your draft work on paper, then plug in your flash drive, transcribe your work, proofread and save to the flash drive. At that computer you can also create a free email account perhaps at www.yahoo.com www.care2.com, www.gmail.com or some other you may know of. That account is from where you can later send your queries. Just make sure you remember to create a password that can withstand a nuclear hit and make sure, since it IS a public computer, to sign out when you leave - every time.
The library will have rules for computer use and accessing the internet. Some have very short periods you can use the computer. Obey the rules. Type fast! Make friends with the librarians.
Oh - a side note - you're in the library, they do have a lot of reference materials. It doesn't work like the net, but it defintely fills a need. Don't pass up that great resource.
2. Second resource: Free Software - Yes there is software out there you can download free (hopefully when you make some money you'll donate to help keep them going). A really great one is Open Office www.openoffice.org Check out the freeware there. They offere a suite of software that does most of what you need. Words processor, spreadsheets for your bookkeeping or query tracking, and several more I haven't had need of yet, but came with the package. The word processor is compatible with Microsoft Word so people can open your .DOCs when you email them. And, if you plan on some self-publishing you can make PDF files with Open Office very easily. They also have lots of templates for things like books and screen scripts. Check it out.
Spacejock offers free software for the writer-especially novels at http://www.spacejock.com/yWriter5.html
Plotbot offers free online screenwriting software http://www.plotbot.com/
3. Third resource: Free Wi-Fi. There are lots of places now that have signs posted offering Free Wi-Fi. Just look around. Coffee shops frequently offer it. Your library may offer computers for use as well as free Wi-Fi. There are even 'hot spots' that offer free Wi-Fi such as bookstores & cafes. Check out your own town with an eye to those places. If you can't buy a cup of coffee try sitting outside and see if the Wi-Fi extends that far. But remember, don't become a problem or an obstruction. If the joint starts jumpin after you arrive and you're taking up valuable table space with one cup of coffee for two hours be considerate: pack it up and come back later.
You're a writer but sometimes you get stuck or just can't get it moving, you need some motivation.
4. Fourth resource: Dr. Wicked's Write or Die: http://www.WriteOrDie.com You can use it online free or purchase a desktop version for $10.00 (no I'm not selling it). Look to the right on the site and you'll see the Write Or Die Online box where you can type in your goal of number of words, your own time limit and a 'punishment' level. It does have sounds so either turn those off or use headphones. You're gonna love it. He now offeres the "Edit Minion" as well.
So now you're rolling, what the next thing you need? Writing work!
5. Fifth resource(s) There are a number of places out there where you can bid for work, check for job postings, etc. There's www.elance.com (lets you make a number of free bids per month - but remember with Elance you're bidding against low bidders so it can be tough to make any serious bucks) and of course you can post on www.craigslist.org offering your writing services. www.writersweekly.com offers advice and market listings as does www.fundsforwriters.com. Most magazine websites list writer's guidelines or submissions under "contact us" or something along those lines. If you want to write for a particular magazine and the masthead doesn't give online contact info check out the editor section, get the address and use snail mail (as primitive as that sounds). You acn also find publsiher listings in books such as Writer's Market, Writers & Artists' Yearbook, Writer's Online Markets and more at your library. Another thing to do while you're there!
These recources should get you well on your way. Plainly, using a bit of creativity and being persistent there are ways out there to get started and earn money with your writing even when you're too broke to put some cash out. Have at it and good luck.