Every computer built in the last 5 years or so has a 3D capable graphics card. Need for Speed Most Wanted has modest system requirements, so it's likely that if you have a fairly recent computer, you'll be able to play it.
You can identify the model and type of your graphics card by going into the device manager. You may also need to update your graphics drivers before you'll be able to play.
As far as your DirectX error goes, I found one guide that gave a hint:
DirectX Error when Installing: When installing the game if you get an error that DirectX9.0c is not installed, even if you've installed DX9.0c already, then find the game's Autorun.exe file (in the base directory of the game CD), right-click on it, select Properties, go to the Compatibility tab, tick the 'Run this program in compatibility mode for' and select 'Windows 2000'. Then double-click on Autorun.exe to begin installation. Make sure to turn off compatibility mode after installing the game.
If this doesn't fix your problem, you're going to have to provide more detail in your question.