There are 3 notable steps that are discussed below.
Initialize the filter by giving it a belief in the state to work with.
This is also knows as system propagation. It uses the system model (literally what it sounds like, a model of the system) to form a new prediction.
Measure and find residuel (with the prediction from previous step) and use it to generate an estimate. This estimate would be incorporating the information from both the actual measurement and the prediction made using the system model.
The probability before incorporating measurements is called the prior.
Once we make a measurement, and know how accurate the sensor is, we scale up the prior (which is a pdf) based on what our measurement tells us.
Since it is scaled, likelihood is not a pdf.
A normalized likelihood, which is a pdf, is called the posterior. It is the probability distribution after we take our measurement into account.