There is no doubt that Blizzard managed to optimize Diablo 3 very well and it can run even on non-gaming laptops almost on full details. The game looks great even on such devices.
As in many recent released video games, the Shadow quality seems to eat the most of the resources, even more than Anti-Aliasing.
If you play Diablo 3 on an older PC, turn the Shadow quality to low or none if the PC is very very old. Notice in-game that after hitting the apply button, the game will turn black for a few moments and will come back with the new adjusted shadows.
The Shadow quality is mostly the only thing that should be changed except Anti-Aliasing and Low FX. Run the game with the other details on High, turn Shadow quality to none if you notice that your character is moving slower than normal (means low FPS). If Diablo 3 still runs slow with Shadow quality on none, start to get the other options to low-medium, Texture quality, Physics and Cluster Density.
As you can read the tooltips, select Low FX to increase the performance and reduce the visual quality, turn off Anti-Aliasing (this option is for high end hardware).
Also talking about laptops, connect the power charger if you plan to play Diablo 3 on such device, the game will run slower without it.
A very important thing. If you have more than a monitor and your Diablo 3 character doesn’t move smooth, there is some sort of delay, turn off Fullscreen Windowed and set the option to Fullscreen.