This presentation is an example on how to create your first Twitter network analysis. I don’t go deep in the network analysis side: using this you can create a basic visualization of a search term network.
First, load gephi (http://gephi.org/) from http://gephi.org/users/download/ Gephi is used to visualize, manipulate and analyze networks. It's a very powerful (and cool tool) that has a active developing community.
Then, download NodeXL (http://nodexl.codeplex.com/). "NodeXL is a free, open-source template for Excel 2007 and 2010 that lets you enter a network edge list, click a button, and see the network graph, all in the Excel window."
In short, NodeXL uses your Office 2007 to pretty much the same things as Gephi does but with Excel. We will use NodeXL to import data from Twitter. The reason why I use Gephi is the efficiency and for the more visually appeasing graphs it produces. Feel free to NodeXL, it's also a excellent tool.