Open the File Manager app, go to home, then click the up button at the top. Look for ExtSdCard. If you see something called sdcard, that's the built in memory for the Tab, not the memory card you put in.
Because the Tab is Ice Cream Sandwich, you can't move apps to the external memory like on older versions of Android. They get installed to the built in memory and that's where they stay. The external memory card is good for putting files on to free up memory - things like movies or music or docs, etc.
To transfer things to the Tab, you can use the Kies from your computer or some over the air apps. I use Dropbox a lot to store and transfer files. Also and OTG (On-the-go) adapter is handy for transferring with a USB flash drive. It has the Samsung plug on one end and a USB on the other. I never use Kies anymore - just Dropbox (with wifi) or the OTG.
There's lots of OTG adapters out there - on Amazon or ebay, etc. The OEM Samsung one is pricey but you can find cheaper ones that work just as well. I bought some at Fry's if it's near you.