I'm a generalist, should I find some sort of niche? Or should I raise my rates to attract better clients?
Use existing knowledge of some narrowly specific type of business to give you intimate knowledge of the unique concerns those people have, how they talk about it, and what boundary conditions are going to affect which solutions do and don't fit well (e.g. gourmet pizza joints near college campuses, or heritage language schools to steal a previous patio11 example).
If you don't have that sort of knowledge already, talk to people until you do. If you do have that sort of knowledge already, keep talking to people anyway because you still have plenty more to learn.
Use knowledge of this specific customer to find, approach, and pitch clients who are a good match for your target customer. If you don't know how to find them, you don't know them yet.
Then, pitch them:
"You can have me do X which will cause money to happen for you."
"I'm aware that you have concern_a and concern_b, which I will handle using specific_approach, whereas generic_person_235089 doesn't even have a clue about these important_issues."
LISTEN to what they say, then use it to refine your ability to select potential clients and to improve your future pitches. Easy, easy, easy hack: remember the words they use to describe things and use EXACTLY those words when pitching them.
Run 10 pitches, review, repeat with another 10 target customers. Make money.
Then, go read tptacek's guide to scaling your practice:
https://news.ycombinator.com/item?id=4247615
P.S. It's okay to be a generalist on the back end. It's not okay to be a generalist when you pitch. Address a clear, specific problem for a clear, specific target customer using clear, specific language which shows sensitivity to the issues as THEY see it and talk about it.
98% of people pitch by talking about things that are really their problems, not the client's problems. Actually, saying 2% of people clear that bar is probably being too generous. If you aren't sure, a good trick is to ONLY use language that you've heard come out of a customer's mouth.
Also, meetups are mainly good for random socialization and free beer. Sometimes networking, but often only incidentally. You need to get way more targeted than "tech people in my area who also want socialization and free beer." Scrounging at meetups is the last resort of people who don't know who their customer is yet.
Being able to find your customer is one of the first things you have to learn about them. And to start out, go about it like you would trying to find any other thing - just, be a lot more determined and creative about it than you would trying to find a local pizza joint to order from.
Say you want to land a heritage language school as a client. Where can you find these people? Where can you find their clients - who might be happy to talk to you at length about which schools in the area are best for people who are concerned about heritage language education?
* Get on Google, Google Maps, Yelp and search for heritage language schools my_city.
* Check forums and trade publications relevant to heritage language schools. If you don't know them, find out while you're learning the other stuff.
* Track down bloggers who write about heritage language education, see if they mention any specific schools / issues, research those. Connect with any users you find in e.g. comments, guest bloggers, etc.
* Guess that many people who are customers of heritage language schools are second or third generation immigrants. Where else can you find these people? Are there churches, community centers, or local shopping resources that also target them?
Find your customers - by way of their customers or competitors if necessary. All of the above probably have something useful to teach you about making your business succeed.
You also want people who will (1) be happy paying you real money if you can reliably produce value, and (2) be more or less content to let you be the expert as long as you're on the ball about producing value and communicating effectively.
You do NOT want cases where people will complain that $20/mo is too expensive, or that a $3 business app doesn't have enough features.
Once you pick an area or two that you have interest in, your first steps should be trying to track down and connect with people. Can you do that? If not, it's probably a bad domain for you. Then, customer development interviews. Learn about them before you work with them.
Existing domain experience from previous stuff you've done in your career is a good starting point. Never worked around real estate agents but have intimate knowledge of how to sell construction companies? That should tell you something about where to look first.
It's a matter of applying conditional probabilities, really. Want to work with barber shops but find that's too general? Okay, what about hipster barber shop owners in their early 30s with a master's degree in English Lit? Now it's suddenly way too specific. Somewhere between the two, you become the ONE person in the city who is right for THEM.
Here is an example. A local lawyer in my community is always holding seminars at local libraries on things like taxes, writing a will, estate planning, etc. These are free informational seminars, so the libraries and village halls basically do the advertising for him. During the seminars, he gives an overview of the topic, and why you might want a lawyer to help with the trickier bits. Now, when some self-selected interested people decide they want a lawyer to help write their will, who is the first person you think they'll call? Maybe the nice helpful clearly-well-informed and capable guy who gives all that free advice at the library?
When you see a free online webinar for a technology topic, this is often what is going on. It's just formalized networking: meeting people interested in X, demonstrating you can provide services Y related to X, and making it known that you do Y for X all the time, and boy is it effective.
I'd imagine you would use your oDesk/elance gigs as a portfolio and get involved in whatever niche community you'd like to work with.
I couldn't comment on the tech market, but many companies may be unwilling to commit to this type of pricing out of irrational discomfort. I think Patio11 has advocated for longer period pricing (weekly, monthly) which might be a good medium between hourly billing and value-based. You're going to get better prices for yourself and your clients will be more comfortable with more familiar pricing.
Personally, I wouldn't attempt to freelance without already establishing a real network outside of work farms like Elance / oDesk. You can still work on side projects and present at conferences while working another full-time job. You can build your presence and authority and if you do a good job, you'll get the type of industry recognition you need to get inbound requests, before you even start advertising your services.
(I want to include the unsolicited caveat that none of this is easy. A less experienced version of myself might have/did read someone else's version of this comment and thought "I should be a software consultant! Thousands of dollars a week! Wow!" when the reality is that you still need people to sell to, you still need to be able to deliver on your promises, and you probably need to offer some level of support and maintenance for whatever you end up developing for your clients. I really enjoy this line of work, far more than a "real job", but it's much more stressful at times and so far--one year in--I'm making less money than I otherwise would be. It's true that the potential upside is greater, but I don't recommend getting into consulting for that reason unless you already have a significant personal network of prospective clients.)