Although my site is a paid site, that doesnt mean you can't have a professional looking site for free!
I know what it's like to
a) Not be allowed to buy a webhosting/a domain, or
b) Not want to buy webhosting/a domain
So here's my tips for making the best site possible, without spending more than your internet bill. Keep in mind, paid hosting has more options than free hosting. Remember: These tips are my opinion, you don't have to read it if you don't like what I'm saying, so don't flame me.

Tip #1: The Layout
The first thing visitors see on a site is the layout, so you don't want some hideous thing jumping out in their face. A lot of people do judge a site by it's layout, so if you really don't think your graphics are good enough for the public to see, don't put it up. Keep practicing creating graphics and you'll really improve. If you really can't make graphics you're 100% happy with, you can still wow your visitors with CSS- graphic skills isn't make-or-break your site. Here are some tips to get your site looking neat and tidier:

FONT:
Make sure the font is readable, easy on the eye. Don't make it less than 7pt, and DON'T use a font like Redensek as your main font. These pixel-y fonts aren't nice to look at for long periods of time. Also, make sure your browser's text size is "Normal" - go to "View > Text Size" to change it.

COMPATIBILITY:
You should be able to view your site in (at the very least) Internet Explorer and Firefox, which are the two most popular browsers at the moment. If your layout doesn't work in both, then those that use the other browser will most likely avoid your site.

Tip #2: Don't chatspeak.
Which means, no u, r or sum1. Just don't. I may seem like a snob for saying it, but it makes your site look unprofessional and its annoying to read. Chatspeak is okay on MSN, but keep it there.

Tip #3: A Good Webhost.
This is the most important step- I suggest you find a host that gives you..
Atleast 20mb of space.
Enough bandwidth for what your site is going to have on it.
No popups. (in fact, no advertisements would be great)
No need for forum posting. (now thats just me, if you're willing to be active on a forum for webhosting- go for it)

I like my hosts to have a cPanel (which is a website manager), its very easy to use. If you have the right version. Most free webhosts have either a..
Web-builder (like freewebs)
Cpanel 5/4 (like ifastnet and phpnet)
Cpanel 10/x (my fave. Like Hostfreeweb)
Xpanel (like 0php)

I suggest you choose the one you feel is easiest for you. If you want to do skinning on your site, it's best to use a host with cpanel x/10+ because it makes life so much easier, and also note that tip #4 will not work if your site uses skinning.
I've tried many, many hosts. The best one I've found is hostfreeweb, because it has no ads, and plenty of space, though it takes about 2 days to get hosting with them. Freewebs used to be a favourite but it does not allow PHP (which comes in handy later) and it now has an annoying toolbar at the top- making the page load slower than it usually would.

Tip #4: Mask domain.
Now that you've chosen a host, you should cover up that icky free, long domain with a much nicer one. I've analyzed (haha, I like that word) some of the free mask domain services that I thought were good and have shown the pros and cons.
co.nr
Example: yoursite.co.nr
Pros: No ads, only requires a button link.
Cons: It can only have co.nr at the end, you cant choose.
I find co.nr to be overused, but it's still a good mask domain place. =)

opt.to
Example: yoursite.girl.to, yoursite.act.to, etc.
Pros: Many, many choices for your domain.
Cons: small, but reasonable add down the bottom of page (although it does load quickly, and you do not need to provide a text link, plus, the ad disappears after a few minutes.)
A lot of downtime.

kickme.to
Example: yoursite.has.it, yoursite.makes.it, etc.
Pros: Once again, many choices for your domain, multiple domains on one account.
Cons: small ad at the top of the page.

unonic
Example: yoursite.net.tf, yoursite.de.tf, etc.
Pros: More than one choice for domain, almost like a real, paid domain.
Cons: unknown- sorry, I haven't tried this one.

Well, thats about all to get started. Now you just need to make a layout/css and content, and you'll be done!