Brush pens are a little like ink painting, a little like pen and ink drawing, and a quick and easy way to write in Japanese or Chinese if you know how. Sold first as Japanese writing pens, they are a great convenience for cartoonists, comic book artists and fine artists -- best of all, they're easier to use than most of the mediums they function like!
First, test your brush pens and just make marks with them. Curving marks, straight lines, narrow lines, wide lines, dots. Try to see how many kinds of marks you can make. If you only have one brush pen in black, that's fine too. If you bought a set of colored brush pens, test each of the colors and draw strokes over other colors to see how they mix. Do a group of marks to show all the colors in your set.
If some of the marks start to look like something specific, don't be afraid to doodle it -- or worry if it's not perfect. This test page should be labeled and set aside for reference, because it'll become your guide to what each of the colors does in combination with the others, what marks you can make with them, and whether each pen performs exactly the same.
Try varying pressure, drawing fast or slow, lifting the pen at the end of strokes, dotting lines, stippling, crosshatching. Any marks you can make with these pens, you'll need to know how it feels and how it looks on the page. I'll use a six color Pitt Artist Pen Terra Set for the demonstrations, but if you have more colors, use them all.
Some brush pens are transparent. Others are opaque. Some have watercolor ink, and water will dissolve, lift and blur the marks. Your brand may be available in 96 colors or more like some water soluble artist brands, or only come in black and brown like some Japanese writing pens with replaceable cartridges that have replaceable points that come with the cartridge.
Label your test page in one of the darkest colors, and try your signature or monogram on it. Brush pens are expressive, and you may have to practice your signature for a while to make it legible if you're used to pressing hard with pens.
Try writing out the alphabet in capital letters, varying the lines for your strokes and using flicking strokes. This can create a style of beautiful brush lettering, calligraphy that's almost Asian in flavor. It's a good exercise because not only will you learn thick and thin strokes, flicking and pressing lightly for straight thin lines, but you'll also gain control of your lettering and be able to do jazzy fancy lettering whenever you like.
Try other styles of lettering that you're familiar with. If you do write in Japanese or Chinese, try writing out some letters and sentences in your chosen language. Brush pens make learning these languages much easier. If you don't have a book on Japanese lettering, try copying some text in a Japanese language manga comic as carefully as you can. Practice the symbols until they become familiar if you're interested in this for language study.
Write out a short poem you like or a favorite saying in brush calligraphy, alphabet of your choice. Drawing letters is important practice for drawing in general, because getting them legible helps establish control of the brush pen. Adults often forget that writing begins with drawing letters -- and that is still drawing.
Get a book on Japanese ink painting, sumi-e, purchase one or borrow it from the library. Look up "The Four Gentlemen," which are the four classical teaching subjects of Japanese ink painting. They are beautiful and useful in many kinds of brush drawing and painting, so try them with your brush pens.