I typically use 8x 2-fold dilutions. If it is a drug I've never tested before I will often run 3 or 4 different dilution series and choose the series that gives the best curve.
If you are running the assay in 96/384 well plate format 10x 3-fold dilutions will give you a good range of concentrations, plus a blank well and a minus enzyme well. This helps to maximise the efficiency of running the assay plus minimises the number of plates required.
The less concentrations you test the larger will be the deviation. The absolute minimum is three, but for more sopund data you should test five or seven.
It is easiest to use a 96 well plate assay and make dilutions across the plate. 7 dilutions of the inhibitor and a zero concentration control. You can make substrate dilutions in the other direction or down the plate.
Answering your question. The minimum is two, but the more the better.
What is more important is having at least one concentration with an effect higher than 0% and lower than 50% and another concentration with an effect over 50% and under 100%. No matter the number of points, if you don't have this two points your estimation would probably be wrong.
You choose the two points closest to the 50% effect, transform dose into log (dose) and fit this two points to a linear curve. This way you will have an estimation of the ED50 very close to any other method with any number of points.
However, in order to safe time, and as long as the design of the experiment allowes it, I use 5-11 concentrations and fit them to an Emax sigmoidal curve. Usually you will get R2>0.99
I have a further question to add: how do I select the maximum concentration in these dilution series if I do not have any prior knowledge on the potency of my compound?
@Engi Hassaan you can search on literature about your compound and the doses that were used or if your compound is something new you can try with various doses and then to increase or decrease the concentrations respecting your first results