Anime and manga are two very different industries. Creating a seamless moving image is vastly different from laying out a dynamic page composition for a page in a manga. With this in mind, I will cover the different jobs you might take in each industry, and what they would involve.
As a semi-professional manga artist, I have more experience with the rigours and needs of the graphic novel. So let's cover manga first.
The Manga Industry
The benefit of manga is one person can perform all of the following roles, if s/he is talented enough. If your skill lies more in drawing than in writing, however, I suggest you team up with someone.
The writer is responsible for creating the story, characters and script of the manga. Scripts can be as detailed or loose as you like. Some writers like to specify camera-angles for each and every panel, others rely on the artist to create the effect they are looking for.
Getting a job as a writer is relatively difficult: you can try http://digitalwebbing.com/talent or apply to individual small companies such as NDP Comics (http://www.ndpcomics.com/).
The artist is usually responsible for the entirety of the page layout, artwork, and overall 'feel' of the manga. Being able to draw a variety of settings and characters is useful, and being able to sequence art is a skill often overlooked. You should be able to draw a character over and over again.
Grayscale, or colour is usually added by the artist, but can be delegated to another person in some companies, such as TokyoPop.
Most manga are black-and-white, so the colourist is more likely to apply grayscale. Originally, this was transparent sheets with a dot print that simulated grey that could be stuck onto the art to give it depth. Many artists have switched to digital tones however, which has opened up a lot of new techniques. Photoshop is the tool of choice.
Colour is obviously used for covers and pin-ups. This is the role that I perform, and therefore one I know quite a lot about. The best way to get accepted into a manga team is to create a portfolio showcasing your best work. Black & white work can be found here: http://artcorner.org and here: http://www.frozenlilacs.com/ (Please note that you should ALWAYS credit the original artist)
Most of my work I have found through http://digitalwebbing.com/talent, or by independent people who have found my website. There is a certain amount of luck involved, and you must be prepared for rejection.
You have a manga - how do you get it published?
If you have created a team, and produced a manga, but you aren't contracted to any publishing companies: don't worry. Whilst you will need a good submission, there are places that accept independent work. TokyoPop (http://www.tokyopop.com/) is the most famous, and probably your bets bet for manga. Antarctic Press (http://www.antarctic-press.com/) are another. Look around, and you should find someone willing to publish before long.
The Anime Industry
There are a multitude of jobs within the anime industry. Here, I am only going to focus on a few.
This is the artist that designs the characters, the settings, and key frames within the animation. A portfolio would be good, along with some kind of formal training in animation.
Essentially, these are the gophers of the anime industry. These are the people that actually make the movement - by drawing every frame between one pose and the next. Much of this is now down digitally, and again - formal training is your best bet. Look for animation courses at your local college or university.
Voice actors are needed for all English language translations, as well as original anime. You should be expressive, perhaps with some background in drama or theatre. The ability to create different voices is useful (think of The Simpsons, with the range of voices created by one actor), although the ability to sound convincing is the most important thing.
Breaking into the industry is hard. Read this article: (http://www.awn.com/mag/issue2.1/articles/bevilacqua2.1.html) for the insiders view.
Directors essentially hold the whole thing together. They have the overall 'vision' of the piece, and it is their job to get the team to produce it. People skills are paramount, as is dedication and faith in the end result. This is a position that usually is worked up to from within the industry.
Anime needs writers too - producing scripts is a slightly different process from writing a manga, as you have to ensure it flows smoothly, fits into a specified time format, and meets the demands of the people funding it. Anime is expensive. This usually means you will have to sell-out, at least until you are a commercial success.
For those looking to create short anime on their own, there is digital software available. Anime Studio is a program that makes it easy to add movement to your art. This can be a great start to landing a better job, as you can build an effective portfolio without the need for too much funding.
In conclusion, getting in can be hard. The work does not pay well, and in my case remains a second job I do around my 'real' work. There are many very talented artists and writers out there, and all are struggling to become exactly what you hope to be. If you're looking for alternative, but similar types of work, video games require plenty of concept artists, animators and even writers(and the money is generally better). Equally, advertising and public sector infomercials can provide the experience and portfolio weight that is so crucial to landing that first job.
Don't give up - even if your dream does not come true directly, you never know what lies around the corner. Continue to do what you enjoy, even if it doesn't pay the bills. Creating something is an incredible feeling, and one that I would not give up for the world.