If you live in Springfield this can be as easy as saying, "I'd sell my soul for ____," in a sufficiently plaintive voice. Then the Devil (looking rather like Ned Flanders) will promptly show up in an appropriate cloud of brimstone smoke.
Outside of Springfield it can be rather more complicated. If god fearing the would be summoner must reject God in no uncertain terms. (Though he doesn't have to mean it literally. Otherwise we wouldn't get wacky literary fun.) It can be in any language, but Latin or Aramaic gives things the right air.
Then with appropriately ancient book (checked out from the convenient books of evil section at the library) or photocopies in hand the demonologist is ready to chant some rather silly things in one of the biblical tongues. Though if you live in Sunnydale the language does not matter, just as long as you get it right in translation. Foul smelling herbs are helpful, though not marijuana. Old world stuff like monkshood, rue, wormwood, sage, and tarragon are called for in different spells. (Time to raid mom’s spice rack.)
The trouble is that there is an awful lot of bunkum out there, old scratch is not going to show up for just anyone calling. If you’re not a saint (and if you are why would you be making friendly with the opposition?) he probably won’t stir from the couch for your punk ass soul. So it has to be a real spell and a very powerful one. Something built into the universe and probably invoking a real name. Getting a hold of the true name of a demon’s true name is a serious task, much less that of the big D himself.
Now selling your soul to a demon is much easier, but you are not going to get as much. And just as with The Prince of Lies you will probably be screwed by some codicil in the contract. (Though you are more likely to get away with it than with someone as smart as the Prince of Darkness.) If you are really, really good (and lucky) you might pull off a something like John Constantine, cheating the devil of his due by playing him off of other powerful demons or tricking him into drinking holy water. More likely you’ll just end up dead and in hell.
In addition something like John Dee’s amulet of power certainly can’t hurt. There are also other things, like the Seal of Solomon that can be used to summon demons. The original object, not a more recent copy. Last in the hands of Pope Leo X and concealed along with the invocation in a pair of candlesticks.
Similar to the situation in Springfield is the tradition of the Devil just showing up when people are receptive. Ready to make a deal with a person who will be important in his continuing war with JHVH. Though a number of incarnations of Satan have called this ridiculous declaring that he is not "a fishmonger".
De Umbrarum Regni Novem Partis (The book of the Nine Gates to the Kingdom of Shadows) has an encoded method for invoking The Adversary:
It is the animal with the tail in its mouth that encircles the labyrinth
where you will go through eight doors before the dragon
which comes to the enigma of the word.
Each door has two keys:
one is air the other matter,
but both are the same thing.
You will place matter on the serpent’s skin
in the direction of the rising sun,
and on its belly the seal of Saturn.
You will break the seal nine times,
and when the reflection in the mirror shows the way,
you will find the lost word
Which brings light from the darkness.
The pact with Lucifer:
"You will accept the pack of alliance that I offer you, surrendering myself to you. And you will promise me the love of women and the flower of maidens, the honor of nuns, the rank, pleasures, and riches of the powerful, princes, and ecclesiastics. I will fornicate every three days, and the intoxication will be pleasing to me. Once a year I will pay homage to you in the confirmation of this contract signed with my blood. I will tread upon the sacraments of the Church and I will address prayers to you. I will fear neither rope nor sword nor poison. I will pass among the plague-ridden and the lepers without sullying my flesh. But above all I will possess the Knowledge for which my first parents renounced paradise. By virtue of this pact you will erase me from the book of life and enter me in the black book of death. And beginning now I will live for twenty happy years on man's earth. But then I will go with you to your kingdom and curse God."
Practical Demon Keeping, by Christopher Moore
The Club Dumas, by Arturo Pérez-Reverte
Hellblazer: Dangerous Habits by Garth Ennis
Buffy the Vampire Slayer (TV)
The Simpsons Halloween Special IV