I want to second this suggestion, and also talk about why I think it works. I'm going to assume that apathy comes from depression, because that's where it comes from for me, and that's the framework that I use to understand and counteract apathy.
Apathy comes from a lack of willpower. Willpower is drained by making decisions, and limited by depression. To beat apathy, you must regain willpower. To regain willpower, you must successfully USE willpower. The catch-22 is that you can't do the things which regain willpower when you don't have willpower. But like @Isherwood says, do ANYTHING. ANYTHING you do will have the side-effect of regenerating a bit of willpower once you've gotten yourself to do it.
Willpower is a finite resource that each of us needs to be able to do things that we don't "want" to do. When willpower is lowest, it can be very difficult to do anything. When someone is depressed, their willpower is depressed: literally pushed down and prevented from the normal process of regenerating to full. Certain activities can help regenerate willpower, but without enough willpower to perform those activities, we get stuck. Vicious cycle, spiral of depression.
How can we break that cycle? Psychiatrists say, "Take these antidepressants; they'll make you feel good enough to start doing things again.". This is one way of breaking the cycle. The chemical burst of artificial willpower is useful, and for some people, it's the best option. But I think it's important to distinguish between what the drug does and how it helps. Taking the drug doesn't "fix" the depression, it puts you in a state of mind where you can more easily do the things you need to do in order to get out of the depressive cycle. The cycle could be broken in other ways.
So, in summary, when willpower is low, we get caught in a downwards spiral of apathy and depression. To get out of that, we need to 1. recognize that we're limited by a lack of willpower, and 2. do anything we can do with the willpower that remains, no matter how simple or small the anything is.
So go outside and DO THINGS! :)