Yes it is possible to get internet access in your property and under Spanish Law they have to be wired in all rooms but you pay a monthly contract
Because there are good mobile phone signals onsite one route for occassional type holiday users are the internet dongles where the best option seems to be the Vodafone PAYG version because you pay for download and the credit does not run out
Youi can get these fron any Vidafone shop, cist around €50 including €30 credit but buy one in Spain and not the Uk as you will pay higher roaming charges