In your channel editor if you click your deforming object and look down under inputs there will be a blendShape sub section, click on this and it will expand to show two or more attributes, one is called envelope and the rest represent the names of different blend shapes you have.

The envelope is a multiplier for the contributions of the blendshapes, so if this is 0 no matter what you do there will be no effect. If it is 1 you will get the exact result of the other different blend shape sliders added togeather. If it is two you will get double the result etc etc.

So first of all make sure the envelope is set to 1 to get predictable results, then as you animate the other sliders the orignal object will change.

You can animate all you blend shapes this way, or you could use set driven key if you want some kind of non-linear result.

If you just want to have an attribute on a controller / your mesh to drive the blendshape for you instead of having to always dig around your geometry to animate it, just make a float attribute in the attribute editor on the object you want and give it a range of 0 to 1. Then load this object into the connection editor on the left hand side, then select your blend shape node (you can do this by graphing your deforming mesh in the hypergraph and selecting the blendshape node, or by navigating to it and clicking select in the attribute editor) and load it into the right, then simply click you custom attribute on the left and then the blendShapeName under weight> 'blendShapeName' on the right.