I started with the same situation. I am currently a college student in the western suburbs of Chicago, and started officially last year. Im majoring in Air Traffic Control and that has nothing to do with this business.
The year before (2010) I helped a buddy out that had about 20 residential lawns and did it with a 22" mower from the back of his truck. I took over his cash business while working another job and made it official in 2011. Quit my other job, still going to school full time and made it a really successful business already (I believe)
I would recommend to get a small truck like a dakota to start with, maybe sell you car? But you dont have to, everyone starts somewhere. Make sure you do have a trimmer, thats a must, a blower helps, but a broom will do if your waiting a few weeks for cash flow.
As for advertisement, take advantage of the flyers you can create on word or something. I printed them out at school because they were free. I have received around 7 people this year alone from craigslist, using the college student idea. vistaprint.com is amazing, join their email subscription and you get 90% of everything for free just pay a little higher for shipping because its coming out of Canada. I used Adeasprinting.com for the doorhangers and ordered 5,000 for a great price. So far that has grabbed a bunch of people.
You can do it!!!
If you have any questions feel free to PM me.
I forgot to mention to start a website for free, you can do that with a bunch of free sites. Just google it. Mine is from webs.com I purchased a domain name now, check it out if you want. llclandscaping.net