In this After Effects tutorial, Devin Page covers how to animate gradient overlay on text.
First, you'll want to just create a new composition, make sure the time and stuff are right.
Then, you just want to create a new solid, it can be any color. Then you want to go to 'effects'. You can just go to your windows if you don't see it, and type fill. You should see 'fill' right underneath here. Just add that to that, and then you could really choose any color. It doesn't really matter. Just whatever colors you want for your little gradient.
Next, you want to make sure you're selecting this, fill, and then you want to use the pin tool to create a little wave or really any shape. It should mask that.
Next, you want to press F on your keyboard. You should see the feather option, and you just want to drag that until it's what you prefer. I usually go around 300.
Next, you want to add turbulent displace. You can just type in "turb", and should be right there. You just want to hold alt and click on 'evolution' right at the effects control. Now you should see all this nerd stuff pop up. You just want to type in "times", and I'm going to type in 400, but the higher you go the faster it will obviously be. If you just play that, you can see it moves a little bit, but my computer's slow. Yeah, it moves a little bit.
You can also change the amount of everything, if you want, like the size. I'm going to turn that to 300. See that movement? It's pretty nice.
Next, you just want to duplicate this layer. I recommend chasing the colors of your layers, just because it's easier to tell them apart. Then you just want to drag it down a little bit, and then you can change the color from right up here on your fill effect. Again, pick whatever colors you want. Usually, I try not to go with colors that might mix up and become super muddy, so usually, I go opposite from the color scale or something like that. Then just duplicate this as many times as you want.
Just keep dragging it down, changing the color. I'm just going to do three colors, but I'm going to select them all and then drag them up higher just to fill out more of the screen. Obviously, if you do more colors, you can fill up the whole that way, too. Then we're going to select all these and pre-compose those because it makes that a lot easier. You can usually name that.
Now, you can just turn off that layer real quick, and add whatever text you want. I'll just put my name. Usually, it'll be like this for your composition settings, but if you right-click the top of here, then go to columns, and go 'mode', you should be able to now see your alpha mats and stuff. You would want to select for your gradients, alpha mat, whatever your text was.
When you turn this on, it should... Maybe if you do it with this text center, it should just play it through that now you can let it render and then play through.
Here's a link to the final result: