If I understand your question correctly, you’re going to want to use the Stroke effect. Create a solid or adjustment layer, trace your lines using the pen tool, then apply Stroke. Animate the Start and/or End point, and you’ll be in business.
OR
Depending on how complex your object is, you can also bring your PSD in as a comp, then use the Write-On effect. Just animate your write-on brush tracing out the shapes in question, then set the effect to reveal the layer – this is down near the bottom of the effect controls.
Good luck.