Select the layer of the object you want centered
Press Cmnd + A (Ctrl + A on PC) You should see little lines (or marching ants) going around the border of your canvas.
Click on the Selection Tool. In your (almost) top menu bar (not the one where it says “File”, “Edit”, etc..) you should see a button that says “align horizontal centers”. Click on it.
Now click on the button that says “align vertical centers”. You should now have a perfectly centered picture.
Turn off the marching ants by choosing Select > Deselect