Usually an aging CCFL lamp gives of a pinkish tint, and causes a general loss of luster on the monitor. Otherwise, an aging inverter may cause dimming even if it doesn't still give an outright flicker.
So the regular protocol, since the Inverter is a fairly inexpensive part (if compared with the more costly, in the $ 140-200 range according to the source for a new part, half the price for a used-refurb unit) implies trying a fresh inverter first, then, if the issue persists, swapping the LCD panel.
You could also change the CCFL lamp responsible for the backlight. It's like a small neon, placed in the bottom part of the LCD panel.
But that requires basically peeling the reflective foil behind the panel, used as a "mirror" to reflect evenly the light on all the monitor, desolder a really thin "neon" lamp, resolder a fresh replacement new and replace gently the foil.
To update on your last question:
1. Changing the inverter is easy, but really time consuming, since basically you'd have to strip bare most of your laptop to expose the inverter, including removing the hinge with "Macbook" written on it, since the inverter is safely lodged there
2. Changing the LCD panel is tricky, since you'd have to strip bare most of your computer _and_ strip bare the whole LCD assembly, thus removing the bezel, the hinges, the frame with the Airport Antenna and the iSight assembly, and put all together. Tricky, and time consuming, but doable.
3. Changing the CCFL is a nightmarish experience, especially if you lack (like me) expertise (thus I simply asked a tech to replace my LCD and inverter, when that happened to me). You'd have to go through point 1 and 2, peel the reflective foil from the LCD exposing the CCFL being careful to avoid crumpling it, painstankingly desolder a very thin neon light (the CCFL actually, but picture it in your mind as a thin neon. As frail as a real one) and resolder a new one, crossing your finger to do all well, replace the foil and put all together.
Thus, I'd say the inverter replacement is easy but boring and time consuming, the LCD replacement is tricky, but manageable, and the CCFL replacement is for experts only.
While a new lamp costs $15,00-$20,00 no one without some experience in soldering and desoldering does that.