Offer some kind of small introductory package in the market place to introduce yourself to clients.
i've proven and ranked sites myself on top of serps in particular keywords.
how can i start providing SEO services to others?
bogart is right, you'll need some sort of landing page on a site somewhere that shows what you offer. Then try getting ranked well for related phrases that will bring traffic to that page.
Create a nice website.. explain all your SEO services(link building, content writing, Press release, branding etc) there.. show few of your sites as example.. i would recommend atleast 3 sites ranging from low to moderately high competitve niche, if you can get tops SERPS in a highly competitve niche(dating, web hosting, weight loss, cancer) then great.
I have developed a website where people see my previous work and the websites, i have worked that better rank on search engines. An online portfolio is a nice step to attract the clients, and second option is as said by david-08 is to make profiles and bid on projects like freelancer.com, guru.com etc
I would say, launch a site for you and promote it and get clients for you. Simple