How can I switch the measure a chart or table is using based on a slicer choice?

If you mean something like this:

Then it's all in the data model.  These are the (simplified) two main tables supporting the report above:

In our case, we have three similar but separate pages (and three corresponding measure tables), because the measures have different data types (percentage, currency, and whole number).

Hi ScottG

Please refer to below link and let me know if you have any further queries.

http://www.bipatterns.com/dynamic-powerbi-reports-via-dax/

Measures on a slicer is well explained in this.