Hello,
The padron is much like the electoral roll in England. The area (La Tercia) gets more allowance from Murcia government according to the number of people on their 'empadronamiento'. So, the more names on the register then the more money they can claim.
The easiest place & nearest to go to, is in the 'Centro Municipal' in La Tercia village. This is located next to the new blue covered football pitch. If you walk down the street opposite Dy Vanne bar, the centro is facing you to the left. Inside there is an office (2nd door on left) where you can arrange for your padron. They will take all your details & take them to Murcia to be processed & you can collect the padron the following week. If I remember correctly, you will need your NIE, passport & a bill with your name & address on it. Best thing to do is to take everything you can, just in case. They will copy what they need. A good time to go is in the morning as they close about noon, I think.
Hope this helps, pm me if you like anytime, I can show you where the office is.-Regards-Josie