You can invoke the simple HTTP server with the -m flag like this:

python -m SimpleHTTPServer

This will automatically use your current directory as the document root. It will server files in the current directory and below. It directly maps the HTTP requests to the directory structure.

When you start the server you should see something like this:

Serving HTTP on 0.0.0.0 port 8000 ...

By default, this command will start the HTTP server on port 8000 and bind to any available IP (signified by 0.0.0.0). In most cases, you'll be able to make requests to http://localhost:8000 in order to use the server.