Although tomatoes will ripen off the vine, it will be important to wait until they have started to turn an orange-ish color. Once the tomato starts to take on that orange color, they will be able to ripen equally whether on or off the vine. You will want to avoid picking any tomatoes that are completely green, because they will most likely need another week or two to turn color. It is easy enough to tell when a tomato is too immature because it will have a bright green color and most likely will not ripen.
If a tomato has barely started to ripen while it is on the vine, it will be able to. You will want to make sure that you place them in a fairly shallow box with a temperature that does not exceed 70 degrees. It will also be important to make sure that it is dark because sunlight will not ripen them whatsoever. You might need to wait as long as a few weeks before they will ripen fully, at least enough to be edible. Knowing when to pick tomatoes and when they are ripe is certainly important for those who are growing them in their backyard, because you will need to be aware of when they can be taken off the vine safely.