Cursive handwriting, like other styles of communication, has changed over time. The Palmer method of practicing and learning cursive was popular throughout schools during much of the 20th century. The style was beautifully smooth and elegant but difficult to use correctly when under time pressure. The D'Nealian style of cursive is the modern approach to a handwriting skill that is more decorative than practical, given the advent of computers.
Sit properly. Beautiful cursive handwriting begins with correct posture. Sit with your feet firmly planted on the floor and directly beneath your writing paper. Rest your non-writing arm comfortably on the side of the table or on your lap. Do not support your body weight with a slouched elbow or the palm of your hand. Misappropriated weight will offset your hand movement and balance, leading to sloppy writing.
Grip the pencil correctly, not tighter. Assume a firm but relaxed grip around the lower three inches of your pencil. Stabilize your tool with your thumb and control the movement with your pointer and middle fingers. Use a rubber pencil grip to facilitate correct positioning, if necessary.
Tape the paper to the table, if necessary, to keep the paper from moving. Beautiful cursive is hindered if you have to chase your paper around the table or desk. Stabilizing the paper will help stabilize your handwriting.
Focus on the connectivity and flow of your letters. The D'Nealian style connects all letters through fluid and intuitive points, such as linking the top of the "o" to the top of the "n." Mastering these points of connectivity is essential to flowing and elegant cursive handwriting.
Slant your paper properly. If you are right-handed, slant your paper to the left and vice versa. Slanting your paper ensures proper wrist positioning.