Inverting your body (and sometimes your way of thinking) can help in numerous ways, such as the following:
Gives the heart a break.
Stimulates the endocrine system.
Calms the mind.
Strengthens the core.
Enhances ability to concentrate and remain focused.
Increases body awareness.
Helps with circulation.
To include all of these gains to their fullest, you need to remain inverted 3-5 minutes (according to Yoko Yoshikawa at Yoga Journal).
Yoga Journal's web site offers steps of the most common inversions. If you are a beginner, then too be honest, I wouldn't recommend any of these. They all involve, great core strength, some flexibility, and great awareness. These are wonderful states that come with practice of easier postures.
A common pose used in the sun salutation and found in almost all Hatha classes is called downward facing dog (adho mukha svanasana). This is a partial inversion, as is a standing forward fold. Already you reap some, albeit not all, of the benefits being upside down can bring.
How can a beginner take advantage of these postures? Or what if you have a shoulder injury, or simply don't feel safe inverting while supporting yourself? There are options. Here is my favorite: Legs on wall pose (viparita karani)
One of the keys to remember is that this is a restorative posture; you are not necessarily looking to stretch the backs of your legs. So, feel free to scoot farther away from the wall.
Getting into it, is the toughest part. But once you've figured it out, it's really quite easy. Just start by sitting sideways close to a wall. As you turn, place one leg up and then the other.
Feel free to modify. If the supports cause any discomfort at all, then adjust them, remove them and/or seek out an experienced teacher to help you place them.
Rumor has it that this pose heals whatever ails you. As long as inversions are contraindicated for you (glaucoma, pregnant, heavy menstruation, etc), then give it a try for at least 5-10 minutes. (I usually go for almost 20 minutes.)