Building your portfolio is one of the most important things you'll do when becoming a freelance artist. It doesn't need to be paired with fancy web design, but it's essential to have a way to show people what you're capable of and to communicate your services clearly.
When it comes to putting together a good portfolio, thoughts on the matter will vary from person to person. I'll share what I've learned so far and maybe I can help you avoid having one that's completely wrong, like I once had.
First, ask yourself what you want to do. Do you want to make comics? Illustrate children's books? Be a concept artist? Whatever it is, plan to design your portfolio around that thing. Don't make the mistake of showing as many styles or genres as possible. You want to appear focused and confident in what you do.
Start actually doing that thing. Research it, learn the basics, work on personal projects, and improve your skills. Hold your work to a high standard and save only the best for your portfolio.
After learning fundamentals, make personal style a priority. Competition is fierce in the art world and you'll have to offer something unique if you want to stand out. This can be incredibly difficult, so do what comes naturally to you and don't just copy whatever is trendy at the time.
Your way of standing out could simply be how you draw faces, your color choices, your textures, and so on. Pick something and do it over and over, and continue to push the boundaries.
Organize your work onto a website. Yourname.com or a similar variation would be best. If you can't afford to do this, a free portfolio service will be fine for now. If possible, try to find one that doesn't place distracting ads on your site.
Less is more. A compelling portfolio doesn't need to be flooded with work. You could start with 10 of your best images or maybe even fewer.
Try to maintain a relatively small number over time (I like to have no more than 18 in a section), and remove or replace old images as their quality stops matching your newest work. It's better to have a handful of great pieces than many average ones.
Remember that consistency is crucial. Most of your work should look like it was done by the same artist. Potential clients should have a good idea of what they'll get if they're going to hire you.
And finally, be patient. It will take time for your work to mature and for your portfolio to reach a professional level. Every artist goes through a growing period when they start out, so don't worry if your work isn't quite where you want it yet.
In fact, that's how you know you're on the right track. Growth is something an artist should always strive for.