For example I have 7Y interest rate swap rate and 7Y Fed funds/Libor basis spread. What is the step-by-step procedure to derive OIS rate from these two?
If you're lucky enough that the payment schedules (start/end dates, frequency, day count, business day adjustment etc.) are the same between the fixed leg of the interest rate swap and the "spread" leg of the basis swap, then you can simply use:
OIS rate (%) = IRS Rate (%) - 0.01 * (basis spread (bps))
Otherwise, to do it accurately, you'll need to do a bootstrap the two term structures (possibly simultaneously if there is mutual dependence between them).
[In fact, in the USD case, there is an added complication that comes from the OIS rate being a compounding rate, while the FedFunds rate is an arithmetic average.]