On the side of the memory card there should be a little sliding tab, check this is in the unlocked position (usually indicated by an open padlock) it is always possible that the tab has fallen out, there are ways of replacing it with tinfoil and sticky tape - real Blue Peter stuff but if that's the case a new one for long lasting reliability is recommended - try sevendayshop.com
Another thing to be aware of if you are new to digital cameras, is that even though you have deleted the images after downloading to your computer, they are still taking up space on the card, just that you cannot see them.
What you need to do is to reformat the card IN THE CAMERA. This way it cleans everything off it and you start afresh.
If you just continue to delete, you will eventually receive the message Card Is Full, or similar or it just won't operate.
I always download my camera via the lead rather than removing the card, this way there is less chance of damageing the card or the door covering it.
I have the download lead permantly plumbed into the back of the pc and can also use it for an external hard drive hook up.