Let me clear the difference between daimons and demons:
Daimons are Greek mythological creatures who are said to have come from the Underworld. They are known to be able to appear in different forms, and one type, called the dream daimon, can even appear in dreams and such.
Demons, however, are supposed to be evil spirits who assist someone in something.
As for your question, why do you want to summon a demon/daimon in the first place?
The practical reasons...well some call upon such entities purely for knowledge for knowledges sake while others call upon them for unrealistic, often greedy reasons. To be clear I personally have never summoned any being, but I would compare it to playing with plutonium. If done very very carefully the reaction can be a controlled one with positive benefits. If done haphazardly you end up with a nuclear meltdown. Binding a sentient being against their will is just asking for trouble in my opinion. Unless you have a really good reason and have studied summoning extensively I wouldn't attempt to summon any entity.
Daimons actually and Demons-as Hollyan mentioned, are not the same. They are actually the same, it's just people who believe they're not. Ancient Greeks believed that Daimons come from the Underworld. People in our days believe Demons come from Hell. However ancient Greeks didn't believe in Hell, so essentially Daimons and Demons are the same. Underworld is a different dimenssion than Hell, it's a matter of belief anyways.
There are many different ways to summon Demons, such as Ouija board, channeling and more complicated rituals. You cannot bind a Demon or an Angel. Demons and Angels cannot be bound to objects anymore... If you try to bind a Demon to an object I Promise you will fail and, most likely you will piss of the Demon and then you'll be in trouble...
I don't really care/know anything about Demons, but I will speak on daemons.
I do not know where this idea that daemons come from the Greek underworld is coming from. Maybe you are confusing modern day ideas about demons and the daemon from Greek religion as I do not really recall any sources suggesting this. I could be wrong, and I would love to hear a source for this.
Daemons in mythology come from Homer and Hesiod. Both of these sources mention daemons. Homer doesn't really make a distinction between gods and daemons. Hesiod however suggests the theory of them being from the Golden Age of man. When the world was destroyed, these golden men stayed as beneficial spirits to man kind.
Socrates was said to have had a daemon follow him and giving him advice about things. The way I read it, it seems he had some sort of clairaudience.
Later on in antiquity, daemons did indeed possess people and cause all sorts of ills. There were even ways in which a person could exspell the daemon.. You can see one of these accounts in the PGM XIII. So, it wasn't "evil Christians" taking all the Gods and demonizing them. Daemons were already slowly becoming associated with things we stereotypically assign to demons. You can dig and find the sources yourself, I suggest "Arcana Mundi" as a good source book.
There are also many other daemons mentioned in the Greek Magical Papyrus (PGM).
Plutarch, On the Ceasing of Oracles, suggests that daemons, not gods, were the ones who gave and maintained the oracles (of course the Oracles still came from the Gods). They functioned as a sort of intermediary between them. Think "Vodou" and you'll understand. He suggests this is for all things in the deity mortal relationship, not just oracles. Since daemons are not really immortal to him, their dying was the reason the great oracles, such as the Pythia at Delphi, were starting to dwindle in use.
There is also the agathodaemon (the noble spirit) which is sort of a guardian angel or a Greek form of a Roman's genius for people in Greek Religion. This daemon protects the household, the oikos. He's given worship on the second day of the lunar month. Usually he's depicted as a snake or man holding a cornucopia.
There's a bunch more about daemons, it's an interesting topic. But, I will leave it at this.
NewEnoch is asking also about Daimons, so I will say that working with one could be found in the PGM, but I would suggest not doing so early in your career. If you wanted to honor the Agathodaemon, I don't think you need to summon it or bind it at all. Just start talking to it, address it, give it an offering (wine, olive oil, bread, fruit), build a relationship. The Agathodaemon is a pretty general term, and in my opinion, it could mean any sort of spirit you see as a personal guardian of the household/you (familiars, guardian angels, etc.)
