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I'm thisclose to offering gardener/lawn maintenance services in my area. My husband is supportive, I know the business, I have most of my necessary inventory of tools, and can estimate off the top of my head. But I don't have anything resembling a sales personality...
That seems to be how our local people like that get clients, too.
Why not start by talking to a few friends about your interest in getting going, and see if they can think of anyone who needs some gardening done? Or perhaps offering your services to a local historic house, theatre, or other nonprofit that has a little land which could use sprucing up. You can leave your cards there and use your time while you work there to talk to passersby about your availability.
Don't forget that a lot of people really don't like the sales personality... and will, in fact, run in the other direction when confronted by one. :)
I think the people commenting here are absolutely right; you'll get new work from referrals by your existing customers - and while it make take a little time to build up your base in the beginning, I wouldn't be surprised if you had a full dance card soon enough.
auntbunny, I did something similar from when I was 14 through College. What you'll find is that word of mouth will get you more work than you can do if you are reliable and do a good job. I also did some when I was underemployed about 10 years ago when I first moved out here. What I found is with a friendly positive attitude ("yes, I can do that") people will tell their friends and so on. Print up some business cards, they don't need to be fancy, because your clients will ask for them to give to other people. I think you'll be a flying success faster than you can imagine. Have fun!