Hi Kristin, this actually isn't too hard to do in ArcMap - I'm guessing from what you're doing your data is in raster format. Firstly before you start just note down the maximum and minimum values of the datasets that you will be displaying.
To set the colour ramp right click on your first data layer, click 'properties', go to the 'symbology' tab and then choose 'stretched' from the options on the left, then choose the divergent colour scheme you want to use from the color ramp list (this is probably where you are already).
To change how it is displayed you then need to scroll down to the bottom of the page and find the 'statistics' section. Here there is a dropdown tab which by default is always set to 'from each raster dataset'. Click the dropdown and change this to 'from custom settings (below)'. This allows you to specify your own parameters for how the colour ramp is applied.
Then all you need to do is input your maximum and minimum values that you noted down already in the max and min boxes and change the mean to 0 - it will now use 0 as the centre of your colour ramp. Standard deviation is a bit trickier but to be honest as long as it's similar for all your datasets you can probably just leave that as it is.
To apply the same to your other datasets you just need to ensure they have their colour ramp set to stretched and then click on 'import' at the top right of the window. You can now import the colour ramp from your first layer to save having to manually enter all of the values again.
Hope that helps!