To create a local script, first click the gear icon at the top right of the script window. Click the drop down box and select Local, then click Save. It is important to note that scripts in Local mode run on the server until the script ownership is transferred to a player. Local scripts automatically transfer their ownership to players when the object they are attached to is grabbed or attached to a player. In addition, there is also a codeblock in the Actions tab under the Player section that transfers the ownership to a specific player. Simply drop the codeblock into the event where you want the script to transfer owners, then specify the object and player.

Seen above is selecting the gear icon to change the script settings.

Seen above is the “transfer ownership of object to player” codeblock found in the Actions tab.