Fading an Object in From Left To Right

Use an image mask and a gradient. I suck at explaining things like this but I'll try. Draw a shape around whatever you want to fade and change it to a gradient and use the grayscale preset.
Then select whatever it is you are fading in the layers and press Shift Apple M to create your image mask. Drag your gradient you just created into the image well of the image mask. Then go to the inspector and adjust the controls of the image mask to add or subtract... whatever it needs to be. Adjust your gradient by selecting it in the layers and then control clicking in the canvas and choosing edit gradient. Stretch out the black and white as needed to get the desired fade. Then set keyframes to move the gradient from left to right to achieve your fade.
Hope that helps.

I'd like to add an alternative solution. Maxx's idea may give you more customization but my idea is a shade simpler: I'm not involving a true gradient, but feathering the mask instead.

Draw a mask around your object. It may need to be quite a bit larger than the object in question. You'll know that, once you start playing with.

Animate the mask's control points. I like to set the last keyframe first, where your object is completely visible. Then move the playhead to a prior point in time. Then set another mask keyframe. Now click on the upper right hand point of the mask, hold down shift, then select the bottom right hand point of the mask.

With these points selected, If you then click and drag on the line between these 2 points, the whole right mask edge should move as one. Peel this line all of the way left until your object disappears. If you push play now, the object should sort of "wipe on" from left to right.

One more thing: Mask feather. With the mask selected, the HUD should have mention of "Feather". You'll want to dial this up. But if your playhead is parked at the beginning of the animation or at the end, you're not likely to see anything. So move the playhead such that you're parked between your 2 keyframes, with the object about halfway exposed, then adjust the feather to your liking.

Again, here is where you'll need to determine if the whole mask needs to be larger because you really only want the object to be effected by this "growing right edge". You don't want to see the feathering on the other edges, probably.

Anyway, this is Just another way to skin a cat. Maybe this will help you out.