How long do levies take to replenish?
Throughout most of the game, levies are the core of your army. Especially in the early game, they are superior in both raw numbers and in utilizing the combat frontage. Levies are drawn from all your pops but are primarily made up of peasants.
Levies cost nothing to recruit and can be raised quickly. However, their main drawback is their fragility. Combat quality aside, when troops die, their pops disappear and the dead men can no longer be raised by you. For professional troops, this is less of an issue, as you can train troops from across your kingdom to refill your manpower reserves and upgrade buildings to increase it. Levies, on the other hand, are tied to their province, and when they die, you have to wait for it to naturally replenish.
How long does this take? Levies replenish at a rate of 1⁄240th of their size per month. This means that if a province’s levies get wiped out, it will take 20 years for them to fully replenish. You are unable to raise any levies from a province until it is at least 20% replenished, so it would take 4 years before it contributes anything. This makes levy losses extremely devastating. As your control is centered on your capital, you must take special care to protect its levies, as it is unlikely you can make up for their loss elsewhere.
If you have lost your levies and you need to know how far into their replenishment you are, there is one awkward way to check. You have to already be at war, which hinders its usefulness, but then simply go to the military tab and attempt to manually raise levies from the province in question. As you hover over it, the tooltip will show you what percentage of levies are currently alive. (You needed 50% recovered prior to patch 1.0.10.)

If your levies are replenished, but you are still unable to raise them, there may be other issues at play. See: Why can’t I raise levies?