I've downloaded an e book onto my computer with my Adobe ID but do not know how to transfer it to my Galaxy Tab (Android)?

You should be able to plug your Galaxy Tab into your computer and copy the file over to it using the file explorer on your computer. Try following the instructions at Memory & SD card: Samsung Galaxy Tab | T-Mobile Support under the section Transfer files between computer & SD card

You will need an ebook reading application on your device that supports the Adobe DRM system though. If you look for apps on the Google Play Store try searching for Adobe DRM : adobe drm - Google Play