Install via the Package Manager(apt-get):

Simply add to your packages:

For Sublime-Text-2:

sudo add-apt-repository ppa:webupd8team/sublime-text-2
sudo apt-get update
sudo apt-get install sublime-text

For Sublime-Text-3:

sudo add-apt-repository ppa:webupd8team/sublime-text-3
sudo apt-get update
sudo apt-get install sublime-text-installer

Install Manually via Terminal:

Download from the Sublime Site:

32-bit:

wget http://c758482.r82.cf2.rackcdn.com/Sublime\ Text\ 2.0.2.tar.bz2
tar vxjf Sublime\ Text\ 2.0.2.tar.bz2

64-bit:

wget http://c758482.r82.cf2.rackcdn.com/Sublime\ Text\ 2.0.2\ x64.tar.bz2
tar vxjf Sublime\ Text\ 2.0.2\ x64.tar.bz2

For Both:

sudo mv Sublime\ Text\ 2 /opt/
sudo ln -s /opt/Sublime\ Text\ 2/sublime_text /usr/bin/sublime

Source: http://www.tecmint.com/install-sublime-text-editor-in-linux/

Install Manually via Script:

Check out this nice script on Github(“Install Sublime Text on Fedora.“) that you can run, just make sure to edit the “*.tar.bz2” in the script to download the latest version of Sublime Text!

#!/usr/bin/env bash
# Usage: {script} [ OPTIONS ] TARGET BUILD
# 
#   TARGET      Default target is "/usr/local".
#   BUILD       If not defined tries to get the build into the Sublime Text 3 website.
# 
# OPTIONS
#
#   -h, --help  Displays this help message.
#
# Report bugs to Henrique Moody <[email protected]>
#

set -e

if [[ "${1}" = '-h' ]] || [[ "${1}" = '--help' ]]; then
    sed -E 's/^#\s?(.*)/\1/g' "${0}" |
        sed -nE '/^Usage/,/^Report/p' |
        sed "s/{script}/$(basename "${0}")/g"
    exit
fi

declare URL
declare URL_FORMAT="http://c758482.r82.cf2.rackcdn.com/sublime_text_3_build_%d_x%d.tar.bz2"
declare TARGET="${1:-/usr/local}"
declare BUILD="${2}"
declare BITS

if [[ -z "${BUILD}" ]]; then
    BUILD=$(
        curl -Ls http://www.sublimetext.com/3 |
        grep '<h2>Build' |
        head -n1 |
        sed -E 's#<h2>Build ([0-9]+)</h2>#\1#g'
    )
fi

if [[ "$(uname -m)" = "x86_64" ]]; then
    BITS=64
else
    BITS=32
fi

URL=$(printf "${URL_FORMAT}" "${BUILD}" "${BITS}")

read -p "Do you really want to install Sublime Text 3 (Build ${BUILD}, x${BITS}) on \"${TARGET}\"? [Y/n]: " CONFIRM
CONFIRM=$(echo "${CONFIRM}" | tr [a-z] [A-Z])
if [[ "${CONFIRM}" = 'N' ]] || [[ "${CONFIRM}" = 'NO' ]]; then
    echo "Aborted!"
    exit
fi

echo "Downloading Sublime Text 3"
curl -L "${URL}" | tar -xjC ${TARGET}

echo "Creating shortcut file"
cat ${TARGET}/sublime_text_3/sublime_text.desktop |
    sed "s#/opt#${TARGET}#g" |
    cat > "/usr/share/applications/sublime_text.desktop"

echo "Creating binary file"
cat > ${TARGET}/bin/subl <<SCRIPT
#!/bin/sh
if [ \${1} == \"--help\" ]; then
    ${TARGET}/sublime_text_3/sublime_text --help
else
    ${TARGET}/sublime_text_3/sublime_text \$@ > /dev/null 2>&1 &
fi
SCRIPT

echo "Finish!"