Drawing cartoon people can be fun and entertaining, especially if you invent your own characters. One thing you will notice is that styles of cartoon bodies vary widely from comic strip to comic strip. Some cartoon characters have floppy arms that look more like noodles, while others have huge, ridiculously muscular arms. Legs can be anything from elongated noodles to stiff, boxy-looking things that would never be realistic. When drawing cartoons arms and legs, there are no real rules -- simply think up a look that fits your character and go for it.
Study the drawing styles in several comic strips or cartoons. Note the arms and legs, especially whether they are somewhat realistic, are overly rubbery, or exaggerated in other ways.
Mimic the drawing style of several comic strip characters' arms and legs, especially the ones that do not appear realistic, by sketching them on paper. Draw the entire comic strip character to improve your proportional drawing skills. Sketch the arms and legs from memory over and over on another area of the paper.
Draw the arm and leg styles from Step 2 on another sheet of paper, positioning them in new ways, such as with arms straight, completely bent, or arms and legs positioned as if the character was running. Exaggerate the positions and motions as popular cartoons and comic strips often do.
Design new cartoon arms and legs by drawing a medium-sized stick figure on a fresh sheet of paper. Sketch the arm and leg shapes around the stick "skeleton" to create simple cartoon appendages. Practice this technique until you have a style of your own.
Draw your own cartoon creations on a fresh sheet of paper; simply start drawing and see what comes out naturally. With time, you will be drawing cartoons that look more polished and professional as your skill set increases.
Besides simply studying comic strips, try drawing some of the characters from your favourite comics. This will hone your skills and help you draw believable characters. Note the motion implied in some comic strip panels; copy those techniques for added realism in your art. If you find one particular style of appendages is difficult to draw, try tracing them a few times until you become more natural at drawing them freehand.
Some cartoons and comic strips are far more detailed than others and require anatomical knowledge to pull off the look correctly. (Superhero-style characters would fall into this category.) In this case, practice drawing as much as possible and study books about drawing the human figure. This style of drawing is based more in realism than it is in cartoon technique.