Elasticsearch require Java, so first install that. You can install java with the help of Synaptic Package Manager or by:

Add Java PPA to apt:

sudo add-apt-repository -y ppa:webupd8team/java

Update packages:

sudo apt-get update

And then install java:

sudo apt-get -y install oracle-java8-installer

Now java is available on your system, So lets proceed for installing Elasticsearch

Import the Elasticsearch public GPG key into apt:

wget -O - http://packages.elasticsearch.org/GPG-KEY-elasticsearch | sudo apt-key add -

It may ask for password for executing sudo command.

Create the Elasticsearch source list:

echo 'deb http://packages.elasticsearch.org/elasticsearch/1.4/debian stable main' | sudo tee /etc/apt/sources.list.d/elasticsearch.list

Update packages:

sudo apt-get update

And then install Elasticsearch:

sudo apt-get -y install elasticsearch=1.4.4

Now Elasticsearch is installed. To restrict the access only to local system add a line to your configuration file elasticsearch.yml.

sudo vi /etc/elasticsearch/elasticsearch.yml

and then uncomment the network.host option and replace it with:

network.host: localhost

Start elasticsearch by:

sudo service elasticsearch start

If you want to start elasticsearch on bootup then execute:

sudo update-rc.d elasticsearch defaults 95 10