First of all, what you wear. Almost all universities' graduation involves wearing a black gown and a hood. In Cambridge, each college's gown can be subtly different from those from other colleges, e.g. Trinity gowns are dark blue instead of black. The higher the degree you're receiving, the more impressive your gown. What your hood looks like, specifically the type and colour of material used to trim it, also depends on what degree you're receiving. For a B.A. degree, which is what nearly all undergrads get, the hood is lined with white fur. (Fortunately Ryder and Amies supply only fake fur hoods.)
The women get off fairly lightly: a sensible black skirt and white blouse. The men have a few options, but usually end up wearing a dinner suit with a white bow tie, academic bands (two strips of white cloth coming from the neck down the chest a few inches like an old-style preacher), with the gown and hood on top. All this black cloth gets very hot in summer, particularly as you're buttoned up to the neck.
So far things don't sound too bad. Next is the bit that the tourists like. All the students assemble in their respective colleges shortly before the time appointed to their college, get their clothes checked, form into rows of four and then walk to the Senate House. This looks quite nice, but still sounds normal. Cambridge, however, was built before the invention of the motor car, and so reserves the right to parade its students down the middle of the road. Yes, when I graduated from Queens' we stopped the traffic on Silver Street. When my wife graduated from Newnham, they got snarled up in traffic. The further out colleges get a coach into the centre a bit and then borrow a more central college to walk from.
At the Senate House itself things get very silly. Lots of things are said in Latin, that few people understand, there is much doffing of hats and people wearing unusual clothes. The students stand the whole time and get shuffled about as people ahead of them get done. It reminded me of a cattle market. The weirdest bit of all is just before you actually go forward. You are still in a row of four and huddle round the Praelector, who is the academic of your college in charge of ceremonial things and says a lot of Latin during the ceremony (oh, and they doff their hat quite a bit too). The Praelector then extends a hand towards the four of you with the fingers stretched out. You each hold on to a finger (I kid you not). The Praelector then says some more Latin (which I think means 'and these four deserve a degree too') and then you let go of your finger. I was very strongly reminded of the children's game Poison Ivy. (No-one is supposed to laugh at how ludicrous it is.) The four of you then, in turn, go forward to the Vice Chancellor (or whoever is standing in for the Vice Chancellor).
The VC is sitting on a chair in a red and white robe, looking a bit
like Father Christmas and there is a hassock in front of them. You
go forward, kneel on the hassock, put up your hands as if praying, the
VC clasps your hands and says 'oh go on then, have a degree' (in Latin),
you then get up (taking care not to tread on your gown as this would make
you fall on to your back), bow to the VC and then walk out of the building
on to the lawn. On your way out you are handed your degree certificate
which, for an institution as awash in history as Cambridge, is rather feeble,
almost photocopied. Out on the lawn lots of photos get taken, people
are very proud of you etc.