Ok.... Here goes. It's been a while since I owned an LS3 C6, and longer since I inspected or changed the filter, but if memory serves me....
It's an LS3 in your 2008 Vinnie, not an LS2. BDK previous post picture is a 6 litre LS2 and is different as it requires 2 filters and has clips. Assuming your LS3 still has the stock filter...........
You need to remove the MAF sensor electrical connection, unlock and pull off the front end crankcase vent tube where it connects across from the MAF sensor, loosen the hose clamp holding the intake tube on to the throttle body. Now the entire intake filter assembly should lift right out (evenly). (The two plastic hold down rivets connecting the assembly to the plastic top rad cover should just pop out when you lift the intake housing up). Don't forget to plug the MAF and vent tube back in, and tighten the hose clamp when you're re-assembling... (You may be able to remove the intake tube ahead of the throttle body (the most forward hose clamp), which would negate having to disconnect the crankcase vent tube, but that's not how I use to do it. I duded up a picture a bit for you. Hope it helps. It's really easy once you've done it the first time.