To delete an application on your iPhone, simply keep your finger tapped on an icon until you see that it has a "shake effect". After that, tap again on the X circle corresponding to that application and it should be removed. This is the only way to delete apps on your iPhone device.
Additionally, connect the phone to computer and transfer all your music, images, videos, etc. This will free your storage as well. After the upgrade, you can transfer them back, depending on how much storage you have left.