Installing Magento 1.9.1 on Bitnami Nginx Stack

First download the Bitnami Nginx Stack Magento.
Install the Bitnami Stack where you like, called by me root_nginx_stack.

After installation copy the demo project to the apps folder and remove htdocs folder

1. cd root_nginx_stack
   cp -r docs/demo/ apps/magento
   rm -rf apps/magento/htdocs
   unzip magento-1.9.1.0.zip
   mv magento root_nginx_stack/magento/apps/htdocs
   
2. change in root_nginx_stack/magento/*.conf all reference 'demo' to 'magento'
3. in root_nginx_stack/nginx/conf/bitnami/bitnami-apps-prefix.conf add the line
   include "root_nginx_stack/apps/magento/conf/nginx-prefix.conf";
4. in root_nginx_stack/magento/nginx-vhosts.conf add the lines below before the include directive

   
       location / {
           index index.html index.php; ## Allow a static html file to be shown first
           try_files $uri $uri/ @handler; ## If missing pass the URI to Magento's front handler
           expires 30d; ## Assume all files are cachable
       }
       
       location @handler { ## Magento uses a common front handler
           rewrite / /index.php;
       }
   

5. in root_nginx_stack/magento/nginx-app.conf replace the location part with the lines below and set your root_nginx_stack path.

   location ~ \.php$ {
       if (!-e $request_filename) { rewrite / /index.php last; } ## Catch 404s that try_files miss
   
       expires        off; ## Do not cache dynamic content
       fastcgi_split_path_info ^(.+\.php)(/.+)$;
       fastcgi_read_timeout 300;
       fastcgi_pass unix:/root_nginx_stack/php/var/run/www.sock;
       fastcgi_index index.php;
       fastcgi_param  SCRIPT_FILENAME $request_filename;
       include fastcgi_params;
   }
   
       ## These locations would be hidden by .htaccess normally
       location ^~ /magento/app/                { deny all; }
       location ^~ /magento/includes/           { deny all; }
       location ^~ /magento/lib/                { deny all; }
       location ^~ /magento/media/downloadable/ { deny all; }
       location ^~ /magento/pkginfo/            { deny all; }
       location ^~ /magento/report/config.xml   { deny all; }
       location ^~ /magento/var/                { deny all; }
   
       location /magento/var/export/ { ## Allow admins only to view export folder
           auth_basic           "Restricted"; ## Message shown in login window
           auth_basic_user_file htpasswd; ## See /etc/nginx/htpassword
           autoindex            on;
       }
   
       location  /magento. { ## Disable .htaccess and other hidden files
           return 404;
       }
   
   
       location ~ .php/ { ## Forward paths like /js/index.php/x.js to relevant handler
           rewrite ^(.*.php)/ $1 last;
       }
   

6. create a database for your magento installation:

   /root_nginx_stack/mysql/bin/mysql -uroot -p
   ...
   create database bitnami_magento;
   grant all privileges on bitnami_magento.* to 'bn_magento'@'localhost' identified by 'MAGENTO_PASSWORD';
   

7. restart nginx and type in your browser: http://localhost:8080/magento/index.php
   your magento installation starts now!

I got the references for this config from Bitnami Wiki and Magento Wiki.
It's not production ready but helps as a starting point.