Q:

How to change which modules are auto-applied in Darktable?

When I open a raw file in Darktable sharpening and a base curve are automatically applied. How do I alter this? I would like to add lens correction.

A:

Automatic presets would do that, see the section "Module presets" in Darktable's user manual.  Note that you need Darktable version > 1.4 for this to work sensibly with lens correction.  In earlier versions the lens correction did not adapt correctly to the image parameters.
Relevant section from the manual:

A module has an expander bar . Clicking on the name of the module
  expands the module's GUI with all parameters.
In its default setting darktable will only expand one GUI at a time.
  If you click the expander bar of another module, the previous GUI gets
  collapsed. If you want to see more than one GUI expanded, you may
  expand further modules with shift-click  – all previously expanded
  GUIs remain opened. The expander bar behavior on click and
  shift-click, respectively, is controlled by a preference setting in
  gui options (see Section 8.1, “GUI options”).
Expanding a module does not activate it. You need to click the  icon
  to turn a module on or off.
Icon  accesses the module's available presets or creates a new preset
  from your current settings (see Section 3.2.3, “Module presets”).

