Model conception


I have a basic stats question:
I want to model a phenomenon, and estimate parameters. How many observations would I need, to be as accurate as possible?
I think it might have something to do with the degrees of freedom, but I am not exactly sure how to use this information. From the definition, I have more or less the impression that the more degrees of freedom you have (using independent observations), the more you will be able to have a precise estimation. But I am not sure this is the only thing.
If anyone could explain or send me a tutorial I would be very grateful.
Thanking you in advance,
Best regards