The steps below are the "easy" way to install Redis 2.2 on an Ubuntu 12.04 system. Be aware that at the time of writing this method will install v2.2 of Redis, which is the version included in Ubuntu 12.04.
If you want the latest and greatest Redis 2.6.x features, you'll need to install from source, which is easy to do by following my other blog post - Install Redis 2.6 from source on Ubuntu 12.04 and running as a daemon.
Step 1 - Add necessary repos to your 12.04 system
Ubuntu 12.04 needs packages from the extended 'universe' to install Redis, so lets add them with
echo "deb http://archive.ubuntu.com/ubuntu precise main universe" > /etc/apt/sources.list
Step 2 - Install Redis
Next, install Redis.
apt-get update apt-get -y install redis-server
That's it. You might want to tweak the Redis settings, in which case edit /etc/redis/redis.conf accordingly.
Good luck. Feel free to comment and ask questions.