How to edit PATH in order to change path of a directory?
If you want to add it to the path ...
export ANDROID_HOME=~/android/sdk/
export PATH=${PATH}:$ANDROID_HOME/:$ANDROID_HOME/tools:$ANDROID_HOME/platform-tools
If you want to replace tools and platform-tools by it ...
export ANDROID_HOME=~/android/sdk/
export PATH=${PATH}:$ANDROID_HOME
In both versions it is added at the end of your $PATH. I assume the / missing in the last part of your question is a typo.
You need to add that to ~/.profile (or ~/.bash_profile if you do not care about other shells than bash).