Getting rid of my SD card
If you've installed any Apps on the SDCard, you can simply move them back to internal storage via the Settings&rarr;Apps&rarr;Manage Apps menu, walking your downloaded apps one by one and see whether it is installed on SDCard. This should be your first step.

For the remaining files: If your device offers an "internal SDCard", you could simply use a file manager like e.g. ES File Explorer File Manager to move "normal files" from the external to the internal SDCard.

Both steps done, remove the SDCard (either should down your device to do so, or simply use the Settings&rarr;Storage menu to unmount the card first if you can access it without shutting down the device).

Optional step: Once the card is removed, you could check again if you still can move apps to SDCard, as the device might use the internal SDCard for this.