This is a question that I receive very frequently. The answer is... it depends (everyone loves that!).
In this case, it really depends on a number of factors: 1) what you feed your worms (that is, the type of food) 2) whether you put the food in whole or chop it up and 3.) how warm the soil is. Note that these are all factors that you can control. I will describe the factors in greater detail below and tell you how to speed up the process (assuming that is what you want to do).
1. Type of food that you feed your worms
This may or may not be obvious, but the types of food you regularly feed make a big difference on how quickly your vermicompost will be ready to harvest. Consider strawberries and potatoes left out on the kitchen counter. In 3-5 days the strawberries will turn to mush and be covered in a grey, fuzzy mold. In that time the potatoes have only gotten in the way and even after a few months all that will happen is that they may turn a bit green and sprout from a few of the eyes. The same thing in your worm bin-- some foods (like tree fruit) decompose really quickly. Whereas other foods (ground contact veggies and fibrous food) breakdown very slowly. Every family will have a different mix of food that breaks down at different rates, so only you can estimate how quickly the foods that you typically add will decompose. If you want to make things go very quickly, add more foods that break down quickly.
2. Surface area of the food
If you chop/grate/mash/slice or otherwise make your food smaller (more easily accessible for decomposition), it will breakdown more quickly. For some foods, this includes freezing or heating the food to break the cell walls prior to placing it in the worm bin. For example, squash breaks down more quickly when cooked and leafy greens turn to mush after freezing. In general, if you juice your food (everything going into your bin is pulp), your worm bin can be ready to harvest in as little as 60 days. If you want to make things go very quickly, increase the surface area or break the cell walls using a food processor/blender and/or heat/freeze before adding to your worm bin.
3. Soil temperature
Soil temperature dictates the activity of the worms as well as the other organisms that assist in the decomposition of the food. In general, warmer temps make the process go more quickly. I recommend your soil temp remain between 65-75F to prevent problems. Temps above 75F can rapidly move into the 90+F range which will most likely kill your worms. I recommend a soil thermometer and a gentle warming method (like a root heater for seedlings). If you want to make things go very quickly, warm your worm bin soil up to 70-75F.
So if you want to speed things up, now you know what to do.