The title says it all, need a web designer to help me fix up a basic wordpress site for free. There might be compensation for further work.
You'd better get a free WP theme, and go DIY with Google+StackOverflow support. A slightly bit harder, but you'll get much more understanding in the long run. Looking for a web designer that would work for free, even for a very basic WP site, in these kind of times? I can only say 'Good Luck'.
I felt tempted to do this, but I wanted to see where it went first. I mean, wouldn't r/choosingbeggars also fit at this point?
If you're using the free wordpress blog at wordpress.com, this is a non-issue. You get it, as is with a choice of themes. You can't customize it. If you make your own wordpress at your own hosting, just get one of the many plugins. It's free and you don't get people snickering at your request. If you expect someone to build your wordpress up from the ground up, well, you're asking a lot, man. That's a lot of work.
If by basic you mean the free wordpress blog, just pick a theme and start posting. Anything with a header navigation and a sidebar for information (if you need it) is nice. I personally like Lovecraft.
For the most part, anyone who is willing to work for you for free isn't going to give you anything better than what you'll get from a good free theme and a couple plugins.