An obvious way to start a campaign, and a mechanism very like that of plots much loved by fantasy authors, is to simply announce as the party gather round that they have been transported as of now, as is and as dressed, straight into the fantasy world. This is probably best for shortish high fantasy campaigns, as no opportunity to role-play anyone other than themselves, but many players will enjoy this for a shorter period.
The extent to which they are exactly themselves can be varied. Within the fantasy world they might suddenly find they have special powers, items on them (eg pens, house keys, rings, etc) might be mighty items (as in Thomas Covenant series) in the new world. Can also have tranformations from skinny literature student to muscle-bound hulk with a innate sword-fighting skills. I'd stick with personalities and particularly their real knowledge being unaltered.
Language is special one. What I would do let them be aware that what they hear other people speak is a strange tongue but within themselves, they can understand the speech (except for words special to the fantasy setting that wont translate). Eg "Graco" might be a monster from the GM's drug-crazed imagination - they might get descriptions of Graco from NPC or find out the hard way but it wont translate. With a little practise, they will find they can speak back but not words that dont translate. Eg "semi-automatic rifle", "saltpeter", and "bidet" might be good words that fail translation!
A typical opening might be telling them, " the room suddenly fills with mist, and you feel the chill of an autumn night. Slowly the mist clears and you find yourselves together within a circle of standing stones below a bright night sky of strange stars. A eerie green fire licks at the standing stones but even as you watch it grows dim and dies. You are obviously in a high place, with deep valleys below you. Small clusters of flickering lights indicate these are inhabited. As you look around to try and get your bearings, you eyes are drawn to a dull light hanging over a mountain far away. Sometimes red, sometimes greenish, the light seems somehow unwholesome. You become aware of dark figures beyond the stone circle..."
Swinging this on players gathered to plan what do to and stopping the narrative at that point is probably best way to introduce it. Enough has been said to rouse the players curiousity. If they like the concept, you can get into gritty detail of deciding what changes to make in the transition (if any), high or low fantasy, assigning game values to their own characters, etc.
Some thoughts on character death needed. Players are playing themselves and are obviously likely to feel the world events somewhat more personally than playing a made up character. Re-introducing a PC in another character isnt quite the same either (but could be done, especially if the player didnt enjoy playing themself). One option is to have players body slowly turn to mist. To get the player back again should involve returning to gate, expending gross power, and some drawbacks for the player concerned.
High fantasy ("we have brought here to save the world") is probably best setting but only if player enjoy a little railroading. A much freer campaign could begin with hearing an NPC beyond the standing stones say: "Oh (expletive fails translation)! This isnt who we wanted!". They cant be sent back but arent going to be persuaded to save the world either.
The real fun in this campaign setting comes from players trying to use their 20th century knowlege and technology in the fantasy world. I wouldnt rule any technology out but would be very tough on adjudicating whether player efforts would work or not. Playing fair, they should not bring in knowlege from reference works that they didnt have in their memory at the moment the game started. (A good reason for making the start a surprise and then arguing for it). Ie they would have to know he formula for gunpowder etc. off top of their heads when the game started to attempt it. Of course, the GM can make life a little difficult without being obstructive with a little care about what is in the game world. Eg (on gunpowder again), saltpeter wont translate. Game world has never heard of it. Even if players knew the gunpowder formula, do they know how to find or make potassium nitrate? Likewise, steel (as opposed to wrought iron) may not be a known technology. Do they really know enough engineering and metallurgy to create a furnace to produce it? Of course, GM needs to bone up a bit on medieval technology but since this is fantasy, only what the GM is confortable with need be there. Consistancy is the thing.