How to update rails? Getting too many errors

I am new to rails, I was working on my first rails app (http://ift.tt/IsdtVd) When i try to edit a latest post, I get an error because Patch method is not available in rails 3.2.16. Then I tried to use PUT method, But i got an error:

(wrong number of arguments (1 for 2)

I am trying to update gems using:

gem update

but it is giving error like this on many packages:

Updating rails
Building native extensions.  This could take a while...
ERROR:  Error installing rails:
    ERROR: Failed to build gem native extension.

        /usr/bin/ruby1.9.1 extconf.rb
checking if the C compiler accepts ... yes
Building nokogiri using packaged libraries.
checking for gzdopen() in -lz... no
zlib is missing; necessary for building libxml2
*** extconf.rb failed ***
Could not create Makefile due to some reason, probably lack of
necessary libraries and/or headers.  Check the mkmf.log file for more
details.  You may need configuration options.

Provided configuration options:
    --with-opt-dir
    --without-opt-dir
    --with-opt-include
    --without-opt-include=${opt-dir}/include
    --with-opt-lib
    --without-opt-lib=${opt-dir}/lib
    --with-make-prog
    --without-make-prog
    --srcdir=.
    --curdir
    --ruby=/usr/bin/ruby1.9.1
    --help
    --clean
    --use-system-libraries
    --enable-static
    --disable-static
    --with-zlib-dir
    --without-zlib-dir
    --with-zlib-include
    --without-zlib-include=${zlib-dir}/include
    --with-zlib-lib
    --without-zlib-lib=${zlib-dir}/lib
    --enable-cross-build
    --disable-cross-build


Gem files will remain installed in /var/lib/gems/1.9.1/gems/nokogiri-1.6.6.2 for inspection.
Results logged to /var/lib/gems/1.9.1/gems/nokogiri-1.6.6.2/ext/nokogiri/gem_make.out

My current gem list :

actionmailer (3.2.16)
actionpack (3.2.16)
activemodel (4.2.3, 3.2.16)
activerecord (4.2.3, 3.2.16)
activeresource (4.0.0, 3.2.16)
activesupport (4.2.3, 4.2.0, 3.2.16)
arel (6.0.0, 3.0.3)
builder (3.2.2, 3.0.4)
coffee-rails (3.2.2)
coffee-script (2.4.1)
coffee-script-source (1.9.1.1)
diff-lcs (1.2.5)
erubis (2.7.0)
execjs (2.5.2)
hike (2.1.3, 1.2.3)
i18n (0.7.0)
journey (1.0.4)
jquery-rails (3.1.3)
json (1.8.3)
libv8 (3.16.14.11 x86_64-linux)
mail (2.6.3, 2.5.4)
mime-types (2.6.1, 1.25.1)
mini_portile (0.6.2)
minitest (5.7.0)
multi_json (1.11.2)
polyglot (0.3.5)
rack (1.6.4, 1.4.7)
rack-cache (1.2)
rack-ssl (1.4.1, 1.3.4)
rack-test (0.6.3)
rails (3.2.16)
rails-observers (0.1.2)
railties (3.2.16)
rake (10.4.2)
rdoc (4.2.0, 3.12.2)
ref (1.0.5)
rspec (3.3.0, 3.2.0)
rspec-core (3.3.1, 3.2.3)
rspec-expectations (3.3.0, 3.2.1)
rspec-mocks (3.3.1, 3.2.1)
rspec-support (3.3.0, 3.2.2)
sass (3.4.15)
sass-rails (3.2.6)
sprockets (3.2.0, 2.2.3)
sqlite3 (1.3.10)
strong_parameters (0.2.3)
therubyracer (0.12.2)
thor (0.19.1)
thread_safe (0.3.5)
tilt (2.0.1, 1.4.1)
treetop (1.6.3, 1.4.15)
tzinfo (1.2.2, 0.3.44)
uglifier (2.7.1) 

Can anyone tell me a way to update rails (or every gem) to its latest version?

Current:

• rails version : 3.2.16
• ruby version : 1.9.3
• gem version: 1.8.23