The engine's oil and filter need to be changed on a regular basis.  How frequently you change your oil depends on your driving habits / driving conditions, the number of miles you've driven between oil changes, the amount of time between oil changes, and the type of oil that you're running.  My shop manual recommends that my oil be changed every 3,000 miles.  

Synthetic oils may last longer than conventional oils.  Oils in engines that are road-racing or towing boats up Pike's Peak may need to be changed more frequently that oils in engines that cruise on an empty highway every other weekend.  Even if you've only driven 30 miles on your current oil but it's been 5 years since you've last changed it, you may wish to change it again.

When you change your oil, you should also change your oil filter.  LS4s from 2005 - 2006 do not have a built-in check valve whereas LS4s from 2007 - 2009 have the built-in check valve.  You'll want to be sure to get the correct oil filter for your particular engine.

Personally, I use Mobil 1® 5W-30 Synthetic Motor Oil and have no complaints.  If you're new to working on your car and you want to get your hands dirty, changing your own oil is a great place to start.  If you do decide to have somebody else change your oil, try to work with somebody who you already have a good relationship with or, at the very least, watch them like a hawk as they work on your car.