Where is the pcv filter located on a 2003 Silverado 5.3 liter? how do I replace the original filter?

Hi!!
The PCV valve is located on top of the Valve Cover, it is held in place by a rubber grommet and has a vacuum hose connected to it. The PCV valve can be easier to remove if you just pull the vacuum hose (with the valve attached) straight out and then remove the valve from the vacuum hose. Here is a picture of the PCV valve for easier identification.
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The pcv ( positive crankcase vent ) filter is typically mounted on top of a valve cover with a hose going to the air cleaner housing side. remove that hose, then pull up on the filter. It should pop right out unless the grommet is hardened, in which case you'll need to replace the grommet too. Be careful if you take out the grommet - it could lose a piece in the motor which could cause serious trouble. The grommet usually comes out clean, so if you're cautious you shouldn't have that problem. To locate the pcv, inspect your motor looking over both sides of the top rectangular "boxes" ( where you put oil in the motor) for that hose I mentioned earlier.