The max output current can be 1A.. any simplest way just using the 7815 and 7915 regulators with a single 24VDC source to get the +15V and -15V?
You can't get there using your given parts.
abs(15)+abs(-15) = a 30 volt difference. Your source can only create a 24V potential difference. Linear regulators (the 7815 & 7915) can only reduce the
magnitude of the voltage... e.g. a +15V regulator needs more than +15V to create a stable 15V output, say 17V or more. Similarly, a negative linear regulator can only reduce the magnitude of a negative voltage, so to create -15V, you need -17V or more. In order to create your +15/-15 rails, you'd need something closer to a 36V supply (36/2 = +/-18, which can be linearly-regulated down to +/-15V nicely).
If you are stuck using the 24V source, and can implement your circuit such that +/-12V rails are sufficient, then using the virtual ground circuit that IanP mentioned would work. Just be sure that you don't connect your virtual ground (24/2 = 12V) to TRUE ground.
If you could drive the system from an AC source, then you could use a center-tapped transformer to generate a + and - AC voltage, then rectify them to + and - DC voltages (two full-bridge rectifiers, one +, one -).
There are many options, it just comes down to what trade-offs you can work with.