Connect the black lead to ground. If you connect it to -5 and +5, that would be a 10V difference and would probably kill the probe. Don't try to probe negative or +12V lines with it.
As long as you know what to expect, it's useful. It can certainly tell you if the clock inputs are working (flashing lights), and if the +5 and gnd pins are good. You can poke at data and address lines to see if any communication is going through the system. For instance, the RFSH, M1, and MREQ lines from the processor should always be blinking. Any clock line should be blinking. If any data or address line is making it to the chip, chances are it will be blinking too. The higher address lines (A15 through A10 or so) may not be too active, especially without a cartridge in.
Chip selects are trickier though, as they will only go low when that particular chip is singled out for communication. The ROM chip's CS pin will probably be blinking though, possibly even both SRAM chips. Audio and video output won't be digital, so who knows what the probe would say looking at any of them.
As a start, look at U22 pins 2, 4, 6, 8 and 10. They should be blinking. Same for U8 pins 6, 5, 8 and 9. Just for grins, U8 pin 13 should be high and pin 7 should be low, though it's because these are hard-wired to power and ground respectively.
U7 pin 4 should be blinking. Pins 11 and 12 should be low and U7 pin 10 should be high.