1. Make sure your background processes are not hogging your CPU/RAM
(Advanced Users) Check your msconfig
2. Make sure your sound/video drivers are up to date
3. Go to CNET and search for 'Process Lasso' and download it (I can't provide links to a 3rd party program, you have to find it yourself)
a. Once installed find 'DiabloIII.exe' and right-click it and change Set Current Priority Class to 'Real Time'
b. You might receive a notification telling you that your PC will automatically change this setting to something lower if it needs to. Hit ok.
4. Boot up the game, run it without sound if possible. Running it with sound seems to cause more stuttering, but should still be playable.
Hope this helps