Most Western ritual magicians use variations of the pentagram and hexagram rituals. In the Golden Dawn tradition you have the Lesser Ritual of the Pentagram and the Lesser Ritual of the Hexagram, in the Thelemic tradition you have the Star Ruby and Star Sapphire, in the Aurum Solis tradition you have the rituals for raising the Wards of Power, and so forth. The normal way this is taught is as it appears in Donald Michael Kraig's Modern Magick, one of the most popular and widely available books on Golden Dawn magick. Kraig says that you start off just using the Lesser Banishing Ritual of the Pentagram and then move on to using the Lesser Banishing Ritual of the Pentagram followed by the Lesser Banishing Ritual of the Hexagram at the beginning of every ceremonial ritual. The Golden Dawn taught both banishing and invoking forms of these rituals, but Kraig sticks to the banishing versions and a lot of ritual magicians are taught to do the same.
I started researching these ritual forms years ago and was confused by how little material was available on the invoking versions and when they should be used. In Aleister Crowley's Liber O vel Manus et Sagittae it is kind of a curious fact that he covers the Lesser Banishing Ritual of the Pentagram followed by an explanation of the Lesser Invoking Ritual of the Hexagram. I went ahead and decided to try this combination out even though most writers will tell you that you shouldn't use the rituals that way. I was absolutely blown away by the result - all of a sudden my practical magical work got a whole lot better. I set up a number of objective tests and, sure enough, the LBRP/LIRH was amazing. I couldn't get anywhere near the same result with the LBRP/LBRH - even though the only difference between the banishing and invoking forms is the direction in which the hexagrams are traced. When I discovered this I asked around and, sure enough, most of the magicians who I knew who were able to get good results using the Golden Dawn forms had figured out the same thing. Other skilled magicians I know have tried the combination at my suggestion and also found that it just works better.
So what is going on here? I think that most modern writers don't understand how to use these rituals. From a Hermetic perspective the Lesser Ritual of the Pentagram represents the psychological realm or microcosm and the Lesser Ritual of the Hexagram represents the physical realm or macrocosm. Together the rituals set up a space in which the relationship between microcosm and macrocosm is defined that I call a field. The four combinations of the banishing and invoking forms of the two rituals set up four different fields that are useful for specific magical operations.
Banishing Field (LBRP/LBRH): This is how most magicians begin their rituals when working with the Golden Dawn forms. It is, in effect, the "full shutdown" - it clears mental and spiritual forms from both the interior and exterior worlds. In can be used to completely cleanse a temple, banish spirits permanently, or neutralize a magical effect that is targeting the magician. What it also does, though, is shut down any ongoing spells that the magician has running unless they are bound to talismans or some anchor other than the magician's consciousness. If you are casting a spell that you want to work over the next week, don't end the ritual with this combination under any set of circumstances unless you're convinced you made a mistake and want to stop the spell. The effect that you just set in motion will be negated when the field goes up.
Invoking Field (LIRP/LIRH): This combination energizes all ongoing magical effects, and can be used to begin a ritual that you want to operate in both the interior and exterior worlds. A good example of this is a spell to get a good job. You want the spell to affect your psyche in such a way that you seem more confident and capable, but you also want it to shift probabilities in the material world so that the right opportunity will come your way.
Centering Field (LIRP/LBRH): This combination sets up a field in which the interior world is engaged while influences from the exterior world are neutralized. This field is ideal for exclusively psychological magical work of all sorts.
Operant Field (LBRP/LIRH): This is the one that I use the most. The field clears the interior world and then merges it the with the exterior world, setting up a space in which thought can more easily become material reality. All of the energy of a spell cast within this field is targeted on the macrocosm and the resulting probability shifts show that magick done this way just influences the outside world better - significantly better.
If you would like, try it out and see, and let me know how it goes. I think you'll be impressed.