Block is actually fairly easy to level up fast. All you have to do is find a group of enemies and just stand there and absorb the damage with you sword or shield. Should you not have a shield I would suggest killing the archers first, if there are any, because they just take your health down and you cannot block incoming arrows with a sword.
You can’t press the block button with something heavy and just leave it there because they actually flank around you and you won’t be blocking them any more. I also suggest that you increase the difficulty because for the leveling up it counts the amount of damage that got prevented by blocking rather than the number of blows that you have blocked.
The master level trainer, chief Larak of Mor Khazgur can be found in the north west of skyrim. It is highlighted in the image below: