The first thing that you need to do is decide what you want to do. While many people know that they hate their current positions, they might not have a clue what else they want to do. If you don't know what you want to do, then you won't be able to make a successful change. Many people have quit their jobs knowing that they want a change, but they have no idea what to do once they're unemployed. If you map out a strategy of where you want to go next, you're much more likely to reach it.
The next step that you need to take is getting some sort of training or education in your chosen field. If you know nothing of the field you're going to get into, then you won't have a very good chance at getting involved in it. This part of the process will probably take the longest. You'll have to fit in some learning time outside of your regular day job. This will require you to take night classes on many occasions. If the job that you want requires a degree, it will take even longer. However, you should know that it is still possible. In fact, many people do this every year. Just because it seems like a lot of work doesn't mean that you should shy away from it.
The next step that you should take involves trying to get some sort of experience in your chosen field. This doesn't have to be a huge thing, but it can help you get a job in a competitive market. If there is an opportunity to intern in your spare time, go for it. It will give you a leg up on the competition.
Once you're prepared, its time to start job hunting. Design a professional resume that will highlight your best features. Once you've done this, you need to hit the pavement. Get out there and use every means of job hunting available. The internet is a great tool, but you shouldn't rely on it as your sole means of job search. Call companies that you would like to work for and ask if they have any positions. Talk to your friends and family and see if they know of anyone looking for work. There are many opportunities out there that the average person will never find because they aren't looking in the right places. Just get your name out there and if you fit the criteria, someone will hire you.
Overall, making a career change is a big step in your life. While it might seem crazy at first, if it makes you happier, that is the key. Go after what makes you happy.