Yes you can. I am 24 years old, recently graduated, degree in programming and I have been simply blown away by web/graphics potential. I have only been into the web for a year. I have a friend who brings in so much business he has to turn people away. Of couse I'm there to pick them up when I can. I think you must look locally, there is a lot out there if you do your homework. If your a self-starter and have the entrepreneurial mindset, you can accomplish a lot. What I did was I would try to target local companies that have old out-dated websites (preferrably horrible ones) and contact them for a redesign. They usually bite and if not, they have my card, which is a vital part of my freelance work. Failure is apart of anything.

I also did jobs for free to build up my portfolio in the beginning, I just asked to have a link back to my site. I think if you make people happy, give them a good site time in and time out, word of mouth will bring in new clients. 90% of my work comes from my customers referring me to people they know. I'm lucky to do the majority of my work from home. There are a lot of home based web jobs listed on my cities craigslist every week too. Just things to consider. Good Luck!