nginx does not support dynamic loading of modules. You need to add ngx_pagespeed as a build time dependency, and to do that you have to first build the pagespeed optimization library.

First build mod_pagespeed, following these instructions: http://code.google.com/p/modpagespeed/wiki/HowToBuild

Then build the pagespeed optimization library:

$ cd /where/you/built/mod_pagespeed/src/net/instaweb/automatic
$ make all

Then move the mod_pagespeed directory to a parallel directory to your ngx_pagespeed checkout:

$ cd /path/to/ngx_pagespeed
$ mv /where/you/built/mod_pagespeed /path/to/mod_pagespeed

Now build nginx:

$ cd /path/to/nginx
$ auto/configure --add-module=/path/to/ngx_pagespeed
$ make install

While ngx_pagespeed doesn't need to be anywhere specific in relation to nginx, the mod_pagespeed directory and the ngx_pagespeed directory must have the same parent.

How to use

To your nginx.conf add to the main block or to a server or location block:

pagespeed on;

Then fetch a page and note that it adds a comment:

<!-- Processed through ngx_pagespeed using PSOL version 0.10.0.0  -->

That's all it does so far.