I just downloaded the icons from http://www.entypo.com
Say I want to just get the lightning bolt icon, how do I get that specifically from the PSD file, and since it's vectored, at the resolution I want?
You find the icon that you want from the thumbnails in the layer list. You can Alt + click that layer to make only that one visible on the canvas to confirm that this is the one you want. You right click the layer you want in the layer list, choose Duplicate layer, in the dialogue that opens up you choose New file in the dropdown, a new tab will open up in photoshop with only that layer present. In the new tab, to make the icon the correct size by pressing Ctrl + T to set the layer in transform state, up in the upper panel you'll see Height and Width parameters (probably shown in percent) you right click inside the text boxes and choose pixels as units and then specify what dimensions you want for the icon. When you export an icon in PNG it will be saved as a raster and not a vector graphic. Click the chain icon between the Height / Width input fields to keep the ratio between height and width. When that is done you can go Image -> Trim to remove any transparent padding that you don't want around the icon.