Research first and foremost, which should identify a problem that you can solve or an issue you can greatly improve. From your research, you should learn about the potential client, their company and market in order to be able to present (verbally or other) this knowledge to the client which will come across a lot more professional than a cold call offering your services (which can also work at times).
Here's how I have gained clients (following research of company/ business/ person/ product/ service) from the most effective method to the least:
1/ Word of Mouth - The single most effective way of gaining clients. A lot of the time, you will have to get the ball rolling by simply asking existing or past clients for recommendations. If you don't have any clients yet, that's fine, start with family, friends, your girlfriend's uncle, haha anyone!
2/ Face to face meeting - Be brave, walk into the workplace, ask to speak with the person of interest for an initial chat (I usually ask for the MD or owner). At this point, even a hello and a handshake can make all the difference. Bring business cards with you in case the person is pushed for time. Bring your laptop with you in case he/she has time to sit down and chat. Obviously the bigger/ busier the company, the less chance you'll get a meeting right off the bat, but they will appreciate the effort you have made to meet face to face, and you instantly become more memorable than a phone call or email. You can't beat human contact, especially in this day and age, it is extremely underestimated.
3/ Phone call - Ring and speak to the person, get straight to the point after introducing yourself, speak with confidence, ask open questions, do not ever ask a closed question; this applies in business as well as anything you want to achieve in life. If you don't do this already, it can seem like quite an arrogant approach at first but you'll get used to it; it is an essential way of improving your success rate/ conversions.
4/ E-mail - This should almost be a written version of your phone call; so again, KISS (Keep It Simple Stupid) short and to the point. The longer the first initial email, the less chance your potential client will read it. This is where you can provide a link or two to your website, or any information you would like your potential client to see in order to gain their interest. Following meetings or phone calls, it is only natural to follow up with an email anyway.
5/ Websites/ Forums/ Directories/ Social Media/ Freelance sites - I'm sure you already have experience with all of these, so I won't elaborate. Some businesses gain nearly all of their customers/ clients from LinkedIn! I wish I was one of those businesses!
Although I have put these methods in order based on my experiences, the trick is to do them all. Yes, a freelance site may not be as effective as a face to face meeting, but the client you get from that freelance site may very well lead to your next client through their word of mouth!