It’s pretty straightforward. The .bashrc file contains settings for your command line. Open it up and add export PATH=$PATH:$HOME/bin to it. This adds the $HOME/bin directory to the end of your path, which is searched for executables. (export will ensure it gets into the environment settings, I accidentally left it out earlier)
Then you add yourself a bin directory to your home, throw scripts in there, and chmod +x them.
Restart your terminal to load the setting (or just enter PATH=$PATH:$HOME/bin directly) and presto, you can now just type Script.sh and it will automatically find and run /home/litppunk/bin/Script.sh for you. Complete with tab completion.
I also put aliases in .bashrc, and routinely add export HISTCONTROL=ignoreboth as well. That one makes bash drop duplicate lines from its history, and also lines that start with a space which I find useful for commands I don’t want to repeat.