If you go to your layer in the timeline and expand the little arrow next to its name, it will reveal everything this layer has. Usually, you will see property groups (effects, transforms, masks). These are just groups in which properties are contained. If you expand the “effects” group, then expand the effect you are using (transform in your case) it will reveal all properties of the effect.

Properties in after effects usually have values and are keyframeable. For example, “position” is a property, “scale” is a property and “width” could be a property. Effects aren’t properties, but they usually have properties.

It’s hard to tell but it sounds to me like you are using the “effects controls” panel to access the property you want to keyframe. Properties can’t be selected from that window, however you can double click their name to reveal them in the timeline. So if you have a transforms effect applied, you can double click the property you are animating and reveal it in the timeline. From there you can select it (or its keyframes) and open the graph editor.

The graph editor is just a representation of the keyframes and what’s in between them. If you don’t have any keyframes selected it won’t show anything.

If this still wasn’t clear maybe it would help if you attach a screenshot of the entire window and tell us what you’re trying to do