First off, always make sure you have the latest drivers for your particular card. You'd be amazed at the number of crashes that are "fixed" by having the player update his gfx card drivers.
Having said that, recently we've gotten a few reports from people who have just downloaded the game for the first time, and get a crash upon trying to start it. It a lot of cases they have an nVidia card in their laptop with a technology called Optimus. This tech basically tries to be smart enough to determine if you really need to use the nVidia card, like for a gfx-intensive task (ie. gaming), or if it could switch to an embedded intel card, for battery savings (for example if you're just checking your email). It switches automatically based on what it decides when you fire up an application.
As you might imagine, when things are automated, they don't necessarily always work the way you expect. Luckily in this case, there is a way to force it to always use the nVidia card for FE/LH.
-Open the "NVIDIA Control Panel" from your start menu.
-On the left, under "Select a task...", open the "3D Settings" tree, and select "Manage 3D Settings".
-Now on the right panel, click the "Program Settings" tab.
-Under "1. Select a program...", click "Add", navigate to wherever your game is installed at (commonly C:\Program Files (x86)\Steam\steamapps\common\Elemental Fallen Enchantress\ ) and select "FallenEnchantress.exe".
-Under "2. Select the preferred graphics...", choose "High-performance NVIDIA processor", then click "Apply" in the bottom right.
NOTE: I found these instructions by using google. Your exact steps may differ, but should be similar enough for you to figure out what you need to do.