There are a total of 4143 items in the game.
When you roll over something you haven't collected yet, the item's name will appear in rainbow colours at the bottom left. Those items are then added to the collection if you successfully complete the level objective.
The vast majority of items will be found naturally while unlocking and playing through every mode in the game. You must do this anyway as every mode will add a new planet to collect in the Wake Up The King! level. I had 98% of the collection done at that point, which meant I only had to manually seek out around 80 more items.
To find the items you missed, I recommend first using this site
to find out the name of the item you're looking for, then searching this thread
to find its location.
You must be a member of the forums to search through the thread's posts.
If for some reason the thread above does not have the item you're searching for, a quick Google search will often come up with a source for the item's location. Just be sure to add in "Katamari Forever" to filter out all the unrelated results.
The most (if not only) frustrating item in the game will be the Cowbear, who runs at high speed around the Cows and Bears level. The main challenge of this item is reaching a size big enough to catch it (7.8m) as there is no eternal mode available. A more in-depth guide on Cowbear can be found here