Increased drop rates are treated as a multiplier to the base drop rate. If you have multiple item drop rate increases, the percentages are added together to arrive at a multiplier. For example, if a player has a 20 lb. Baby Gravy Fairy (50%), Mad Looting Skillz (20%), and a Mr. Accessory Jr. (25%), then the item drop multiplier will be 50% + 20% + 25% = 95%. To find your final drop rate, the game computes the "final drop rate" as
When you finish off a monster the game rolls a uniform random number between 0 and 1. If the number it rolls is less than the final drop rate, you get the item. So, in this example let's say we are farming for chef's hats which have a base drop rate of about 33.5%. Using the equipment above your final drop rate would be
When farming for more common items, a high multiplier may push the drop rate above 100%. This is just treated as 100%.
Here is a table with further examples.
Some mechanics have an item drop bonus that depends on some other character attribute.