It's relatively painless

sudo apt-add-repository add-repository
sudo apt-get update
sudo apt-get install bitcoin-qt

How you get rid of the old copy depends on how it was installed, if it was a default install this will probably get rid of that anyway.

This could be found by searching on google and using couple of different queries, nevertheless. Here we go :

sudo apt-get upgrade
sudo apt-get update
sudo apt-get install build-essential
sudo apt-get install libtool
sudo apt-get install autotools-dev
sudo apt-get install autoconf
sudo apt-get install libssl-dev
sudo apt-get install libboost-all-dev
sudo apt-get install libdb5.1-dev
sudo apt-get install libdb5.1++-dev
sudo apt-get install libminiupnpc-dev

download berkeley db

wget http://download.oracle.com/berkeley-db/db-6.0.20.tar.gz

unpack

tar -xzvf db-6.0.20.tar.gz

now build berkeley db

../dist/configure --enable-cxx

once the process completed

make

and then

make install

now download bitcoin repo from github

if you do not have git installed install it by

apt-get install git

then run

git clone git://github.com/bitcoin/bitcoin

cd bitcoin

./autogen.sh

let it complete

./configure

let it complete

make

now you should have bitcoind in the src folder copy that to usr/bin folder

 sudo apt-get update
 sudo apt-get install -y git-core build-essential libssl-dev libboost-all-dev libdb5.1-                                      f    dev libdb5.1++-dev libgtk2.0-dev

 git clone https://github.com/bitcoin/bitcoin.git
 cd bitcoin/src

 make -f makefile.unix clean; make -f makefile.unix USE_UPNP= bitcoind



 USE_UPNP=1 : build but enable by default
 strip bitcoind

Then run it with

 bitcoind