How to update my Ipodtouch 4gen from Ios 4.2.1 to 6.1?

Connect the iPod to your computer and updae via iTunes. See:

iOS 4: Updating your device to iOS 5 or later

You need iTunes vesion 10.7 or later on the computer.

You can't go to an intermediate version.

Will all my content risk being deleted?

Not if all the synced media like apps and music are in the iTunes library. This is discussed in the link I provided in my first reply

Will my ipod disfunction because it has a very old software 4.2.1 that has not been updated.

Some users reported that iOS 6 slowed the iPod a little. Many apps not requires iOS 5 or higher.

- The first step of an update is iTunes making a backup of the iPod. Note that the backup does not include synced media like apps and music. The backup does included photos/videos taken by and saved to the iPod. Those are the ones in the iPod's camera roll album

- Transfer iTunes purchases to the computer by:

iTunes Store: Transferring purchases from your iOS device or iPod to a computer

In iTunes 11 use Control+B to show the Menu bar then go to iTunes>File>Devices>Transfer Purchases

- For non-iTunes purchases you need a third-party program like one of those discussed here:

Recovering your iTunes library from your iPod or iOS device: Apple Support Communities

I think no more than 100 MB more than other versions.