The Professor is (writing just before the release of All That Remains) widely considered one of the worst IDs.
His ability, like that of Custom Biotics, does not impact gameplay at all, entirely dictating deck construction. (This is different from identities like Andromeda, GRNDL and NEXT Design, which have abilities boosting the start of game, and are inactive for the rest of the game. Notably, Andy is the only one of these three not to have a downside for this benefit.)
He has the lowest influence in the game, at 1, but is the most splash-friendly ID there is: Professor decks generally have more than a third of their deck from opposing factions.
His ability, playing one of any program ignoring influence, allows for a deck featuring three SMCs, along with other shaper tutors and recursion to support the biggest, splashiest programs from out of faction, like Sneakdoor Beta, Keyhole, Medium, Nerve Agent, Imp, or high-inf icebreaking programs like Faerie, D4v1d, Morning Star, Garrote. (All this while not preventing use of low-inf programs like Femme Fatale, Parasite, et al.: you get to have a silver bullet effect running one-of situational cards like Copycat, maybe Crescentus, Deus X)
At present, most Professor decks end up looking a bit like Anarch GoodStuff with Shaper deck manipulation, plus Faerie and Sneakdoor. This is largely to do with the lack of good or high-inf Criminal programs to give more advantage to playing him: Sneakdoor, Faerie, Garotte and Savoir-faire are the only criminal programs with inf >2.
His art shows the hexagons which frame all program cards. This (along with the ability text) is a very unsubtle hint: the Prof is all about the programs. Build a deck which supports and utilises good programs, has memory, econ and speed.
At present, most Prof decks seem to be built around ProCon or Freelance Coding Contract. If you want to go for the latter, it's not too hard to have more than half your deck be programs. This is very fun.
I am ... anomolous in believing the prof is good. But, you know, they say Account Siphon's the strongest card in the game, that it's best when the Corp doesn't see it coming, so the Runner who the Corp will least suspect of running Account Siphon (by virtue of not being allowed it alongside a few other cards) must be the best, right?
The professor, as an identity, will only get stronger as more programs are released. Upcoming cards like "Rex", and non-NRDB spoilers we've seen should continue to give Professors more program options make his ability work.
Three important questions to keep in mind for building your prof deck:
Do you have enough memory and econ?
What (if anything) do you want to spend your 1 inf on? (I'm a strong believer that "nothing" could be an acceptable answer -- deckslots are tight, after all.) Frequent answers include Stimhack, a second Femme or sucker. I've seen people try Easy Mark, BOX-E, a second Cache (I like), a Shard of your choice, Ms. Beckman, Oracle May, Express Delivery and Cyberfeeder.
Are you getting enough out of being the Prof? A big criticism is that a Prof deck will frequently be a worse Kate, or a worse Chaos Theory. Count your influence. Are you playing more than 20-25? Can you work out a way to frame your deck better with other IDs?