Fortunately for you OC'ing graphic cards are waaay easier than OC'ing processors and RAMs. 

Overclocking with stock voltage:

Benchmarking:
~From your stock clocks, 850mhz, just skip to 900mhz (memory clocks at 1300mhz) and take it from there by doing stress test (to see any signs of instability like anomalies such as artifacts, vertical lines, reboot, etc.)
~When you are satisfied with the stability, increase and increment of 10mhz, so 910mhz. Then do the stability test.
~Again when stable, increase by 10mhz to 920, then do stability test.
~Repeat until you encounter instability.
~When you hit the instability mark, decrease by 5 mhz and relatively start to increase the memory clocks from 1300mhz in increments.
~If you still unstable, decrease by increments of 2 mhz untill you are confident with the stability of the card.

24/7 Usage:
Above method is to see your MAX clocks setting that is stable, now for 24/7 usage, you are to factor in the following:
-temperature
-memory clocks

Temperature is prominent in overclocking a card, even though a certain card can overclock pretty high, if the temps exceeds that of  a safe temperature operation of the card, if will reduce it's life longevity.
So for 24/7, you are to prioritized the temps over performance, as appose to benchmarking were to push the cards performance but endure a little heat for a brief amount of time.
So Google up (and ask around this AMD Radeon Thread) and ask around fellow 5770 users what is the safe max LOAD temp when overclocked the card a well s the IDLE temp of your overclocked card. 

Memory clocks is advisable to not be excessively overclocked, but adequate enough to maintain stability when in conjunction with the core's clocks when overclocked.
e.g. If you were to overclock your 5770 Vapor-X to 950mhz/1xxx mhz, you need to find the low stable 1xxx (memory clocks).
Alright, everything what I said are the briefs and highlights of how to overclock your graphic card, do more deeper research and ask around a lot ya! 
I can't help much coz I don't owned the 5770 so I dunno the overclockability of this card, if you own a 5850, I can help you out for sure...