This is how to run a Tahoe node or a complete Tahoe grid. First you have to install the Tahoe source code, as documented in install.html.
The tahoe executable is used to create, start, and stop nodes. Each node lives in a separate base directory, inside of which you can add files to configure the node. Nodes also read and write files within that directory.
A grid consists of a single Introducer and one or more nodes. If you are creating a new grid, you'll need to create both an Introducer and a node (and then invite other people to create their own nodes and join your grid). If you are joining an existing grid (such as the public test grid), the Introducer will already be running, and you'll need to create a node.
To construct an introducer, create a new base directory for it (the name of the directory is up to you), cd into it, and run tahoe create-introducer .. Now start the introducer by running tahoe start .. After it starts, there will be a file named introducer.furl in that base directory. This file contains the URL which the nodes must use in order to connect to this introducer.
To construct a node run tahoe create-client, which will create ~/.tahoe to be the node's base directory. Acquire a copy of the introducer.furl from the introducer and put it into this directory, then run tahoe start. After that, the node should be off and running. The first thing it will do is connect to the introducer and get itself connected to all other nodes on the grid.
Point your web browser to http://127.0.0.1:8123 to use this node.