Professor Ted is Ted 'Theodore' Logan (Keanu Reeves) from Bill & Ted's Excellent Adventure and Bill & Ted's Bogus Journey and Bill & Ted's Excellent Adventures (cartoon series).
Short premise of those movies is:
Excellent Adventure - Bill & Ted are actually rock gods in the future because of their band, Wyld Stallyns. But for now they're members of Wyld Stallyns and high school students in San Dimas, California in 1988, and they're about to fail their final history test. If they do, Ted's dad (Captain Logan, police chief) will ship him off to military school and the band will never reach rock god status. Thus, the peaceful future brought about by Wyld Stallyns music will never exist. So this guy from the future Rufus (George Carlin) gives them a time travelling phone booth and they collect persons of historical significance (and meet some medieval babes that later come to the future and become their girlfriends and band members), bring them to Bill & Ted's present and have one kick-ass presentation that helps them to get an A.
Bogus Journey - Bill & Ted have graduated, but they still aren't good at playing music, but they need to enter a Battle of the Bands to become noticed and famous. Only thing is that a bad dude from the future sends evil robot copies of Bill & Ted back to kill present Bill & Ted. They do, and Bill & Ted go to Hell while evil robot Bill & Ted ruin their lives on Earth. Bill & Ted get out of Hell by beating Death/The Grim Reaper at Battleship, Twister and assorted other games. They go to Heaven and get in by mugging some people and quoting song lyrics at the gates. Then they get to talk to God, who sends them back to life. Bill & Ted, with the help of a weirdass alien genius named Station, beat the evil robot Bill & Ted, get their girlfriends back, use time travel to learn their music in time for the Battle of the Bands, totally kick ass and become rock gods.
The first movie was better, but the second was still neat. The cartoon series followed Bill & Ted on more time travelling adventures. The only thing I'm acknowledging from here is that the San Dimas Elementary School Library is after Ted for keeping Little Red Riding Hood out since he was 5 years old, and that the dudes went on more time travelling adventures. Because really, that's all I remember and I can't find the episodes anywhere.
Anyway, I'm taking Ted from after Bogus Journey, only he's not married. He's sorta on a long-term 'break' from his relationship with one of the medieval babes. After the Wyld Stallyns' first world tour, Rufus decided it was a good idea for Bill & Ted to get some life experience. Bill's off doing his own thing and Ted ended up teaching music at Fandom High.
Ted in Fandom
He's a music teacher. He says 'dude' a lot and will call persons of the female persuasion 'babe' or 'dudette'. He's definitely a child of the 80s. You know the turtle dude in Finding Nemo? Totally based off Bill & Ted.
Ted lives at 18 Apocalypse Avenue in the house with the green roof. His current roomies are Tommy Oliver, Josh Lyman (gone for the summer) and Elle Woods. His former roomies were Autolycus and Rita Skeeter. He's also the caregiver for Earl the miniature giraffe, who lives in the back yard in a specially made giraffe house next to the artichoke garden.
Personality-wise, Ted is very dopey and dense. He's usually cheerful and LOVES Twinkies for the excellent sugar rush they provide. Sometimes he eats a little too much sugar and ends up with a sugar hangover. He's fun-loving, music-loving and completely oblivious.
And he looks like Keanu Reeves with a shaggy hair cut.