Important edit: a database backup before you do any module updating might prevent data loss and is always a good idea!
It is a pretty straight forward process. For Transcribe simply follow the official installation instructions and overwrite the currently installed module files. Find the instructions here:
A more general overview which might apply to most EE 2 or 3 modules: EE 2 and 3 add-ons usually come in a zip file, and the zip file contains a mixture of files and folders. All Add-ons contain a folder with the add-on itself in it - usually at the bottom of a folder stack that replicates the normal folder structure for an EE 2 or 3 installation - so for example an add-on with the name "XXX" might be at the bottom of a folder path like this (EE3 uses a slightly different directory structure):
To install this add-on, simply copy the folder XXX to the equivalent
expressionengine/third_party directory on your EE server.
Some EE2 add-ons also have custom Control Panel code - so you get a customised control for the add-on within EE. For that, you also need to install another folder which is at the bottom of a different folder path (EE3 might have a different path):
To install this, again simply copy the XXX folder to the equivalent folder on your EE installation.
Now is your last chance to do a database backup. When the replacing/overwriting of files and folders is done, go to the Add-Ons/Modules page in EE 2 or 3 and click on the button "Module Updates" (top right) - and then if necessary 'install' the add-on (by clicking on the 'install' button on the row the add-on is listed on).