Here's a list of the ah-ha moments, or the things that will trip you up as you move from Civ4 to Civ5:

• Religions are no longer in-game, but there is a social policy regarding religion which is exclusive with Rationalism.
  
• The hexagon system will take some getting used to.
  
• Roads are no longer needed, except to connect cities together to form a trade network. Do not spam roads willy-nilly but plan them out to lay down as few road tiles as possible in order to form a network between your cities.
  
• A city can work any tile within 3 hexagons. That means you immediately get access to 6 tiles (unless blocked by terrain) surrounding the city.
  
• Culture produced in the city still grows the borders, but only one tile at a time and the AI gets to pick. But you can spend gold to purchase additional tiles to add to your city.
  
• Civ4 you could work a maximum of 20 squares. In Civ5, if you manage to purchase / acquire all 3 rings of tiles around a city, you can work a maximum of 36 hexagons.
  
• Buildings are expensive in Civ5 - choose wisely and limit what you build.
  
• Happiness is now a global thing, if your happiness goes negative it will impact your entire empire not just a few cities.
  
• You can only have one unit per tile of the same specialization. So only one combat unit per tile and only one non-combat unit per tile. Workers and settlers are non-combat and thus can coexist on a tile with a combat unit like warriors or archers.
  
• Archers can attack up to 2 tiles away if they are on a hill (or in other situations). This is called a "ranged" attack and is accessed with the [B] Bombard key.
  
• Most or all ships now have ranged attacks. A barbarian ship along your coastline can how shoot at any of your units within 2 units of the coast. Defend your coastline with a few archers so that you can shoot back.
  
• Cities now have a 2-unit ranged attack that can be used against any enemy unit within 2-units. So a coastal city can easily kill off a barbarian ship with a few turns of attacks.
  
• Cities have built-in defenses, you do not have to specifically station (fortify) a unit in the city.
  
• Be careful with garrison, it pretty much consumes the military unit and makes it a permanent part of the city. The garrisoned unit also prevents other combat units from entering the city.
  
• The "alert" command is more useful then the "fortify" command, because the unit gets defensive bonuses and will wake up when it spots the enemy.
  
• Put your melee units in front of your ranged units with regards to the expected threat axis. Ranged can then fire over the heads of the melee units, softening up the enemy before you attack with melee.
  
• Combat units (all or only some?) create a zone of control around them that is 1 tile in radius. Enemy units are reduced to moving 1 tile per turn within that zone of control.
  
• Units can draw bonuses from friendly units on neighboring hexagons.
  
• Rapid expansion is generally a no-no. You will quickly fall into unhappiness across your empire or run a deficit.
  
• Balanced exploration of the tech tree is a must. Make sure that you pickup happiness, economic, scientific techs at the same rate that you are chasing military techs.