Regarding camera lenses, what do 24-70 mm f2.8, 70-200mm, etc. mean? how do I decide which lenses I need?

The 24-70mm and 70-200mm both tell you the cameras focal length range. Since both of these have more than one number that means they are zoom lenses. In simple terms the small number means wide angle and the large number means telephoto. The 24mm side will let you get a wide area in the shot, the 200mm will let you pull something close in. It gets a lot deeper than that but I'll leave it at that for now.

The f2.8 tells you the largest opening the lens will allow. On many zoom lenses you will see f numbers because that opening size is a ratio and varies with the focal length used. A zoom lens with an f2.8 is usually a pro/high level lens because that is considered a large opening on a zoom lens. The larger the opening the more light that can hit the sensor, the better the camera will work in fast action or dark settings. It takes good glass to handle that size opening which is why many consumer grade lenses only open to f5.6 at the longer length.

The f-stop number can be confusing because on the surface it seems backwards. A small number like f2.8 is actually a bigger opening than f22.

Which lens you need depends on what you are shooting. In general if you need a wide shoot you'd go for the 24-70 while if you needed to pull in something far away you'd go for the 70-200. If you can just have one I'd go with the 24-70 as it will be the best for general purpose shooting.

I agree with the above. For all practical purposes, your 24-70 is going to be your workhorse. You'll use that almost everyday.

The 70-200 is more for telephoto work. I use that lens occasionally (at the zoo, at my kid's soccer game etc).
The good thing is you can buy one now, and later buy another... Start with the 24-70 and buy the 70-200 if you find that you need more zoom.