Values of homes are reassessed at different period in different areas of the state. In St Louis, we're reassessed every 2 years. Knowing the assessed value, however, does not tell you what your taxes will be, because each section of each municipality may have a different tax structure that is then added together to figure out your actual tax. For example, you may be paying a municipality tax, a fire dept tax, a school district tax, etc and each of those may have had something happen during the past year that will change the actual taxing rate.
Your starting point would be to determine what the taxes were last year from the property tax bill, then determine if you were reassessed this past year (you would have been notified and given a chance to contest it), then contact each of the taxing entities that are in the area and may put a tax on the home or property to see if they have had changes and if so what those are, then add them up.
The county or municipality should be able to help you with what the taxes were last year and if there are any changes in the homes assessment for this year.