Spacecraft usually have different electronic boards which serve different functions. Each is usually an independent "subsystem." For example, one usually has a main "Command and Data Handling" subsystem, called the C&DH (or CDH). This is the main interface to the ground: all the telecommands from the ground go to that board (which usually gets a bit stream directly from the TTX), and all the telemetry (measurement points from different sensors and onboard equipment) is routing through the C&DH and then beamed down to Earth to a ground station.
If you want to display data from your Cubesat online, you'll need first to get the data back on the ground and onto a ground control system (or GCS). There a number of GCS available, and which are either open source or proprietary and made to order. Once you've accumulated the data on the ground, you should be able to provide access to a subset of the data to the rest of the world by reading telemetry stored in a database on the ground.
If I may, I would recommend against sharing all the data from your spacecraft. A number of telemetry points are used for health monitoring, and as such, they should not be shared with potentially malevolent actors who may try to exploit that in order to take control of your vehicle.