What's your OS?
What model phone do you have?
Not all phones require software (mine doesn't), but most do. And like Dias de verano said, you'll also need a USB cable. If you tell us your phone's model, we can help you find the software and cable that are compatible for your phone.
It may be possible to keep using your camera. I also use a MicroSD like the one you described, and before I purchased a USB cable, I was using my digital camera. Before you plug the camera into your computer, go through the options and see if there is a setting for USB Mode or Data Mode or anything like that (if you're unsure, you can list the different options). If so, enable it and then plug it in. Then, make sure you actually access the camera's folder via My Computer, as there may be a certain subfolder that you have to use. When you drag and drop a file onto the camera's icon, you could possibly be adding it to the camera's memory rather than the memory card.
