Direct Assignment

When prior information about the parameter is very abundant, probabilities can be assigned directly and subjectively to the values.

Conjugate Distributions to the Model

If the likelihood function is Gaussian, choosing a Gaussian prior distribution for the parameter will ensure that the posterior distribution will also be Gaussian.

Article link

Non-informative Priors

Another possibility for choosing the prior stems from automatic mechanisms that do not insert subjectivity. These are also known as objective or conventional or default priors.

Article link