I am fuzzy on the details and would really appreciate someone who could give me a quick overview. let's say I have theoretically sound reasons for the prior I chose. Now what? what are the actual mechanics from here? according to what i have read; the posterior density is proportional to the likelihood function times the prior density.so, I have my prior density by assumption, and I find my likelihood function by ?? which method? Is finding the likelihood function the part where I have to use a numerical method in the case I don't have a conjugate prior which is analytically solvable?After someone enlightens me on the likelihood function, I multiply it to the density... and have something that's proportional to the posterior. how do I proceed from there?

by the way, let me know if there's something incredibly elementary I am missing so I can go read it and not waste your time.

Read "Probability Theory: The Logic of Science" by E. T. Jaynes