What is the mechanism by which sugars glycate proteins?
One mechanism of glycation is the Maillard Reaction.

The mechanism starts with nucleophilic attack of the sugar carbonyl group by a side chain amino group from the protein.

The Milliard Reaction occurs in the human body and has been implicated in various adverse health conditions.

The cornea, lens and retina are known to be damaged by this reaction.

See The Maillard reaction in the human body. The main discoveries and factors that affect glycation Pathologie Biologie, Volume 58, Issue 3, Pages 214-219 for a recent review.