I would like to learn how to download texts from my phone to my computer please??

TouchCopy is an application that's available for Mac or Windows computers that will do what you want. I like PhoneView for Mac.

You'll need to use a third-party app as Meg suggests to get the text messages off of the device and saved as a file (usually exported in PDF format) to be viewed on the PC.

An iTunes backup will of course backup the texts on the device, but they will only be usable when the backup is restored to the device. iTunes won't extract them to a file on the PC.