There was no single guide that provided this answer, so here’s my own after tinkering around for the entire day on CentOS 5.4.

When I installed CentOS, I did not install a desktop environment, and only added development libraries and tools.

Update your packages
Assuming this is a fresh CentOS install, you’ll want to update your packages:

yum update

Say ‘y’ to every question asked. The update process may take some time depending on the speed of your connection. After this is complete, proceed below:

Download Nginx source
http://wiki.nginx.org/NginxInstall

As of this writing, I downloaded the development 0.8.36 version.

Configre Nginx
Where I have extracted the Nginx source to, I used the compile-time option #3 found at:

http://wiki.nginx.org/NginxInstallOptions

./configure 
  --prefix=/usr 
  --conf-path=/etc/nginx/nginx.conf 
  --http-log-path=/var/log/nginx/access_log 
  --error-log-path=/var/log/nginx/error_log 
  --pid-path=/var/run/nginx.pid 
  --http-client-body-temp-path=/var/tmp/nginx/client 
  --http-proxy-temp-path=/var/tmp/nginx/proxy 
  --http-fastcgi-temp-path=/var/tmp/nginx/fastcgi 
  --with-md5-asm --with-md5=/usr/include 
  --with-sha1-asm 
  --with-sha1=/usr/include 
  --with-http_realip_module 
  --with-http_ssl_module 
  --with-http_perl_module 
  --with-http_stub_status_module

Compile and Install Nginx
In the same directory, perform

make install

To install Nginx.

Create The Nginx Service File

edit /etc/init.d/nginx in your editor of choice and paste in the following:

#!/bin/sh
#
# nginx - this script starts and stops the nginx daemin
#
# chkconfig:   - 85 15
# description:  Nginx is an HTTP(S) server, HTTP(S) reverse 
#               proxy and IMAP/POP3 proxy server
# processname: nginx
# config:      /usr/local/nginx/conf/nginx.conf
# pidfile:     /usr/local/nginx/logs/nginx.pid

# Source function library.
. /etc/rc.d/init.d/functions

# Source networking configuration.
. /etc/sysconfig/network

# Check that networking is up.
[ "$NETWORKING" = "no" ] && exit 0

nginx="/usr/sbin/nginx"
prog=$(basename $nginx)

NGINX_CONF_FILE="/etc/nginx/nginx.conf"

lockfile=/var/lock/subsys/nginx

start() {
    [ -x $nginx ] || exit 5
    [ -f $NGINX_CONF_FILE ] || exit 6
    echo -n $"Starting $prog: "
    daemon $nginx -c $NGINX_CONF_FILE
    retval=$?
    echo
    [ $retval -eq 0 ] && touch $lockfile
    return $retval
}

stop() {
    echo -n $"Stopping $prog: "
    killproc $prog -QUIT
    retval=$?
    echo
    [ $retval -eq 0 ] && rm -f $lockfile
    return $retval
}

restart() {
    configtest || return $?
    stop
    start
}

reload() {
    configtest || return $?
    echo -n $"Reloading $prog: "
    killproc $nginx -HUP
    RETVAL=$?
    echo
}

force_reload() {
    restart
}

configtest() {
  $nginx -t -c $NGINX_CONF_FILE
}

rh_status() {
    status $prog
}

rh_status_q() {
    rh_status >/dev/null 2>&1
}

case "$1" in
    start)
        rh_status_q && exit 0
        $1
        ;;
    stop)
        rh_status_q || exit 0
        $1
        ;;
    restart|configtest)
        $1
        ;;
    reload)
        rh_status_q || exit 7
        $1
        ;;
    force-reload)
        force_reload
        ;;
    status)
        rh_status
        ;;
    condrestart|try-restart)
        rh_status_q || exit 0
            ;;
    *)
        echo $"Usage: $0 {start|stop|status|restart|condrestart|try-restart|reload|force-reload|configtest}"
        exit 2
esac

Save the file.

Register the nginx service

chmod +x /etc/init.d/nginx
chkconfig nginx on

#This portion exists because nginx will not start without it
mkdir /var/tmp/nginx

http://www.hikaro.com/linux/centos/nginx-init-script.html is the original source with some modifications.

Download PHP and Install
http://www.php.net/downloads.php

Extract the source to a directory.

I have my PHP configured with the following options:

yum install libtool-ltdl-devel
yum install openssl-devel

./configure --with-zlib --with-bz2 --with-curl --with-curlwrappers --enable-exif --enable-ftp --with-gd --with-ldap --enable-mbstring --with-mcrypt --with-mysql=mysqlnd --with-pdo-mysql=mysqlnd --enable-soap --enable-sqlite-utf8 --enable-zip --with-openssl

Compile and Install PHP
In the same directory, perform

make install

Copy the php.ini file
Still in the PHP source directory.

cp php.ini-production /etc/php.ini

You should edit the php.ini to match your wanted PHP configuration.

Download Spawn-Fcgi and install
(http://elasticdog.com/2008/02/howto-install-wordpress-on-nginx/ was very useful for this portion)

Spawn-Fcgi comes from the lighttpd project. We are not installing the lighttpd server, but one of the components from the project.

Download spawn-fcgi from:
http://redmine.lighttpd.net/projects/spawn-fcgi/news

As of this writing, I downloaded version 1.6.3. Extract the source to a directory, and change to it.

Configure and install with

./configure
make install

spawn-fcgi should now be installed to /usr/local/bin.

Create the service file for PHP Fastcgi
edit /etc/init.d/fastcgi in the editor of your choice and paste in the following:

#!/bin/sh
#
# php-cgi - php-fastcgi swaping via  spawn-fcgi
#
# chkconfig:   - 85 15
# description:  Run php-cgi as app server
# processname: php-cgi
# config:      /etc/sysconfig/phpfastcgi (defaults RH style)
# pidfile:     /var/run/php_cgi.pid
# Note: See how to use this script :
# http://www.cyberciti.biz/faq/rhel-fedora-install-configure-nginx-php5/
# Source function library.
. /etc/rc.d/init.d/functions

# Source networking configuration.
. /etc/sysconfig/network

# Check that networking is up.
[ "$NETWORKING" = "no" ] && exit 0

spawnfcgi="/usr/local/bin/spawn-fcgi"
php_cgi="/usr/local/bin/php-cgi"
prog=$(basename $php_cgi)
server_ip=127.0.0.1
server_port=9000

#####EDIT THIS TO MATCH YOUR USER AND GROUP
server_user=marketdark
server_group=marketdark
############################
server_childs=5
pidfile="/var/run/php_cgi.pid"

# do not edit, put changes in /etc/sysconfig/phpfastcgi
[ -f /etc/sysconfig/phpfastcgi ] && . /etc/sysconfig/phpfastcgi

start() {
    [ -x $php_cgi ] || exit 1
    [ -x $spawnfcgi ] || exit 2
    echo -n $"Starting $prog: "
    daemon $spawnfcgi -a ${server_ip} -p ${server_port} -u ${server_user} -g ${server_group} -P ${pidfile} -C ${server_childs} -- "${php_cgi} -c /etc/php.ini"
    retval=$?
    echo
    return $retval
}

stop() {
    echo -n $"Stopping $prog: "
    killproc -p ${pidfile} $prog -QUIT
    retval=$?
    echo
    [ -f ${pidfile} ] && /bin/rm -f ${pidfile}
    return $retval
}

restart(){
        stop
        sleep 2
        start
}

rh_status(){
        status -p ${pidfile} $prog
}

case "$1" in
    start)
        start;;
    stop)
        stop;;
    restart)
        restart;;
    status)
        rh_status;;
    *)
        echo $"Usage: $0 {start|stop|restart|status}"
        exit 3
esac

Save the file.

Register the fastcgi service

chmod +x /etc/init.d/fastcgi
chkconfig fastcgi on

Test:

[root@localhost init.d]# service fastcgi start
Starting php-cgi: spawn-fcgi: child spawned successfully: PID: 9146
Starting fastcgi:                                            [  OK  ]

Configure Nginx for FastCGI and PHP
Edit the file /etc/nginx/fastcgi_params

And make sure the file looks like this
(From http://nakedtrout.com/site-performance/nginx-php-fpm-apc-awesome-wordpress-performance/42063

fastcgi_param  QUERY_STRING       $query_string;
fastcgi_param  REQUEST_METHOD     $request_method;
fastcgi_param  CONTENT_TYPE       $content_type;
fastcgi_param  CONTENT_LENGTH     $content_length;

fastcgi_param  SCRIPT_NAME        $fastcgi_script_name;
fastcgi_param  REQUEST_URI        $request_uri;
fastcgi_param  DOCUMENT_URI       $document_uri;
fastcgi_param  DOCUMENT_ROOT      $document_root;
fastcgi_param  SERVER_PROTOCOL    $server_protocol;

fastcgi_param  GATEWAY_INTERFACE  CGI/1.1;
fastcgi_param  SERVER_SOFTWARE    nginx/$nginx_version;

fastcgi_param  REMOTE_ADDR        $remote_addr;
fastcgi_param  REMOTE_PORT        $remote_port;
fastcgi_param  SERVER_ADDR        $server_addr;
fastcgi_param  SERVER_PORT        $server_port;
fastcgi_param  SERVER_NAME        $server_name;

# PHP only, required if PHP was built with --enable-force-cgi-redirect
#fastcgi_param  REDIRECT_STATUS    200;

fastcgi_connect_timeout 60;
fastcgi_send_timeout 180;
fastcgi_read_timeout 180;
fastcgi_buffer_size 128k;
fastcgi_buffers 4 256k;
fastcgi_busy_buffers_size 256k;
fastcgi_temp_file_write_size 256k;
fastcgi_intercept_errors on;

Save the file.

Edit the file /etc/nginx/nginx.conf

My file looks like this:
(Source: http://interfacelab.com/nginx-php-fpm-apc-awesome/)

#CHANGE THIS TO THE USER TO RUN THE SERVER UNDER
user  marketdark;
#####################
worker_processes  1;

events {
    worker_connections  1024;
}

http {
    include       mime.types;
    default_type  application/octet-stream;

    sendfile        on;
    keepalive_timeout  65;

    server {
        listen       80;
        server_name  localhost;

        location / {
            #CHANGE THIS TO THE PATH TO YOUR WEB ROOT DIRECTORY
            root   /var/www/marketdark;

            index  index.html index.htm index.php;

            # if file exists return it right away
            if (-f $request_filename) {
                    break;
            }

            # otherwise rewrite the fucker
            if (!-e $request_filename) {
                    rewrite ^(.+)$ /index.php$1 last;
                    break;
            }

        }

        # if the request starts with our frontcontroller, pass it on to fastcgi
        location ~ ^/index.php
        {
                fastcgi_pass 127.0.0.1:9000;
   
                #CHANGE THIS TO THE PATH TO YOUR WEB ROOT DIRECTORY
                fastcgi_param SCRIPT_FILENAME /var/www/marketdark$fastcgi_script_name;
                fastcgi_param PATH_INFO $fastcgi_script_name;
                include /etc/nginx/fastcgi_params;
        }

        # redirect server error pages to the static page /50x.html
        #
        error_page   500 502 503 504  /50x.html;
        location = /50x.html {
            root   html;
        }

        # pass the PHP scripts to FastCGI server listening on 127.0.0.1:9000
        #
        location ~ .php$ {
            root           html;
            fastcgi_pass   127.0.0.1:9000;
            fastcgi_index  index.php;
            fastcgi_param  SCRIPT_FILENAME  /scripts$fastcgi_script_name;
            include        fastcgi_params;
        }

    }
}

Start nginx
Test:

[root@localhost init.d]# service nginx start
Starting nginx:                                            [  OK  ]

Test your install

Where you have defined your web directory path (where I have it noted #CHANGE THIS TO THE PATH TO YOUR WEB ROOT DIRECTORY) ,
create an index.php file with the following:

Now, figure out the IP of your server and go to it in a browser (for example, since I have my centOS installed on hyper-v under a private NAT, it would be http://http://10.1.10.10/).

At this point you should see the PHP information page!