Well, not an easy explaination. You can try premade apps to do it, but you have to realize sms/mms data, while not fully encrypted, are still custom kept from system to system to provide some protection from dataminers and exploits.
How are your adb tool skills? It's the basic tool-set for reading and writing data from one device to an android device. I would either do a raw dump of the partition, trying to recover over-written data and just run your favorite disk recovery tool, or go straight to the disk recovery tool. Android system and text partitions are less than 20gb total, so it would only take 20 minutes or so to do . And if you are lucky that those blocks have been fragmented and remain unwritten after delete, you can even try to just recover from the directory itself, and leave the rest alone. Sorry that I can only point you in a direction, as every manufacturer, and sometimes every device, can have a slightly different method of accessing data. But that is how you would do it, and whether you NEED root or not, depends on where the actual sms/mms database files are kept and how they are encrypted (if any). Your carrier only keeps logs.
So tl;dr ...
potentially optional: #1) Learn to root, find someone to do it for you that you trust.
#2) Find sms database location.
#3) Attempt file recovery.
#4a) if 3 succeeds, open the old database in your SMS reader.
#4b) if 3 fails, learn every song and dance move from every season of Glee, join a flash mob, and show up at Tribars house for poison lemonade.
www.pandorarecovery.com
